Push a Swing at Its Own Rhythm and a Tiny Push Builds a Huge Swing
Tell natural from damped and forced vibrations, see why resonance builds such large amplitudes and where it is used, separate loudness from intensity and learn what the decibel measures, and connect pitch to frequency and quality to waveform.
Why does a swing go higher if you push it at just the right moment?
Push a child on a swing at random moments and very little happens — some pushes help and some fight the motion. Push once every time the swing comes back to you and the amplitude builds until the swing is going higher than you could have thrown it. The pushes have not got stronger. They have got timed.
Every object that can vibrate has a rhythm of its own — a frequency at which it prefers to swing, set by its size, its mass and its stiffness. A swing has one, a tuning fork has one, a guitar string has one, and a column of air in a pipe has one. That is its natural frequency.
And if you drive the object at exactly that frequency, the small pushes add up instead of cancelling, and the amplitude grows enormously. That build-up is resonance, and it is the most consequential idea in this part of the chapter — responsible for the loudness of every musical instrument, for the way a radio tunes to a station, and for the practice of soldiers breaking step on a bridge.
To get there you need to sort vibrations into three kinds.
- Natural vibrations, at the body's own frequency with no external force
- Damped vibrations, which die away because energy leaks out to the surroundings
- Forced vibrations, at the frequency of an applied periodic force rather than the body's own
And resonance is the special case of the third when the applied frequency happens to equal the natural one.
The part then turns to what makes one sound different from another, and here the language has to be handled carefully. Loudness, pitch and quality are sensations in the listener; intensity, frequency and waveform are measurable properties of the wave. The two sets correspond one to one, but they are not the same, and every question in this section turns on keeping them apart.
This page covers the second part of the ICSE Class 10 Physics chapter on sound: natural, damped and forced vibrations, resonance and its applications, loudness and intensity, and pitch and quality.
Every object that can vibrate has a rhythm of its own — a frequency at which it prefers to swing, set by its size, its mass and its stiffness. A swing has one, a tuning fork has one, a guitar string has one, and a column of air in a pipe has one. That is its natural frequency.
And if you drive the object at exactly that frequency, the small pushes add up instead of cancelling, and the amplitude grows enormously. That build-up is resonance, and it is the most consequential idea in this part of the chapter — responsible for the loudness of every musical instrument, for the way a radio tunes to a station, and for the practice of soldiers breaking step on a bridge.
To get there you need to sort vibrations into three kinds.
- Natural vibrations, at the body's own frequency with no external force
- Damped vibrations, which die away because energy leaks out to the surroundings
- Forced vibrations, at the frequency of an applied periodic force rather than the body's own
And resonance is the special case of the third when the applied frequency happens to equal the natural one.
The part then turns to what makes one sound different from another, and here the language has to be handled carefully. Loudness, pitch and quality are sensations in the listener; intensity, frequency and waveform are measurable properties of the wave. The two sets correspond one to one, but they are not the same, and every question in this section turns on keeping them apart.
This page covers the second part of the ICSE Class 10 Physics chapter on sound: natural, damped and forced vibrations, resonance and its applications, loudness and intensity, and pitch and quality.
What is the difference between natural, damped and forced vibrations?
Natural vibrations happen at the body's own frequency with no help; damped vibrations die away as energy escapes; forced vibrations happen at the frequency of whatever is driving them.
Natural or free vibrations. A body vibrates at its own natural frequency after being disturbed once, with no external periodic force acting on it.
- The frequency depends only on the body — its length, mass, tension or stiffness
- In an ideal case the amplitude stays constant, because no energy is lost
- That ideal case requires a vacuum, since in any medium the body loses energy to it
Examples: a tuning fork struck and vibrating in a vacuum, a simple pendulum swinging in a vacuum, a stretched string plucked in a vacuum. Strictly speaking, truly natural vibrations are possible only in vacuum, and that is the point examiners look for.
Damped vibrations. The body vibrates at very nearly its natural frequency, but the amplitude decreases steadily with time.
- The cause is loss of energy — to the surrounding medium as sound and heat, and to internal friction within the body
- The frequency is practically unchanged; it is the amplitude that falls
- Eventually the vibrations stop altogether
Examples: a tuning fork vibrating in air, whose note gets fainter; a swing left alone, which gradually comes to rest; a plucked guitar string, whose note fades; a pendulum swinging in air.
So every vibration you can actually hear is damped, because hearing it means energy is leaving the body and reaching your ear. A perfectly undamped vibration would be silent.
Forced vibrations. A body is made to vibrate at the frequency of an applied external periodic force, rather than at its own natural frequency.
- The frequency is that of the applied force, not of the body
- The amplitude depends on how close the two frequencies are — small when they differ, large when they are close
- The vibrations continue as long as the force is applied and stop when it is removed
Examples:
- Pressing the stem of a vibrating tuning fork onto a table top, which makes the table vibrate at the fork's frequency and the sound becomes much louder
- The sound board of a guitar or a sitar, driven by the strings
- The diaphragm of a loudspeaker, driven by the electrical signal
- A wooden panel rattling when a machine nearby runs
Why the tuning fork gets louder on the table, which is the standard example. A fork alone sets only a small volume of air moving, so it is faint. Pressing its stem on a table forces the large table top to vibrate at the same frequency, and the table sets a much greater volume of air in motion. The sound is louder but it also dies away faster, because the same store of energy in the fork is now being spent more quickly.
And that trade-off is the boundary case worth stating. The total energy given to the fork by the strike is fixed. Making the sound louder means spending that energy faster, so it lasts a shorter time. You cannot get both a loud note and a long one out of a single strike.
The comparison in one line each, which is what a "distinguish between" question wants:
- Natural: own frequency, constant amplitude, no external force, needs a vacuum
- Damped: own frequency, decreasing amplitude, energy lost to the medium
- Forced: frequency of the applied force, amplitude depending on how close the frequencies are, continues while the force acts
Natural or free vibrations. A body vibrates at its own natural frequency after being disturbed once, with no external periodic force acting on it.
- The frequency depends only on the body — its length, mass, tension or stiffness
- In an ideal case the amplitude stays constant, because no energy is lost
- That ideal case requires a vacuum, since in any medium the body loses energy to it
Examples: a tuning fork struck and vibrating in a vacuum, a simple pendulum swinging in a vacuum, a stretched string plucked in a vacuum. Strictly speaking, truly natural vibrations are possible only in vacuum, and that is the point examiners look for.
Damped vibrations. The body vibrates at very nearly its natural frequency, but the amplitude decreases steadily with time.
- The cause is loss of energy — to the surrounding medium as sound and heat, and to internal friction within the body
- The frequency is practically unchanged; it is the amplitude that falls
- Eventually the vibrations stop altogether
Examples: a tuning fork vibrating in air, whose note gets fainter; a swing left alone, which gradually comes to rest; a plucked guitar string, whose note fades; a pendulum swinging in air.
So every vibration you can actually hear is damped, because hearing it means energy is leaving the body and reaching your ear. A perfectly undamped vibration would be silent.
Forced vibrations. A body is made to vibrate at the frequency of an applied external periodic force, rather than at its own natural frequency.
- The frequency is that of the applied force, not of the body
- The amplitude depends on how close the two frequencies are — small when they differ, large when they are close
- The vibrations continue as long as the force is applied and stop when it is removed
Examples:
- Pressing the stem of a vibrating tuning fork onto a table top, which makes the table vibrate at the fork's frequency and the sound becomes much louder
- The sound board of a guitar or a sitar, driven by the strings
- The diaphragm of a loudspeaker, driven by the electrical signal
- A wooden panel rattling when a machine nearby runs
Why the tuning fork gets louder on the table, which is the standard example. A fork alone sets only a small volume of air moving, so it is faint. Pressing its stem on a table forces the large table top to vibrate at the same frequency, and the table sets a much greater volume of air in motion. The sound is louder but it also dies away faster, because the same store of energy in the fork is now being spent more quickly.
And that trade-off is the boundary case worth stating. The total energy given to the fork by the strike is fixed. Making the sound louder means spending that energy faster, so it lasts a shorter time. You cannot get both a loud note and a long one out of a single strike.
The comparison in one line each, which is what a "distinguish between" question wants:
- Natural: own frequency, constant amplitude, no external force, needs a vacuum
- Damped: own frequency, decreasing amplitude, energy lost to the medium
- Forced: frequency of the applied force, amplitude depending on how close the frequencies are, continues while the force acts
What exactly is resonance, and where is it used?
Resonance is the special case of forced vibrations in which the frequency of the applied periodic force equals the natural frequency of the body, so the body vibrates with a very large amplitude.
Why the amplitude grows so much. In ordinary forced vibrations the driving force is sometimes helping the motion and sometimes opposing it, so the energy fed in is partly cancelled. When the two frequencies match, the force is in step with the motion at every cycle, so every push adds energy and the amplitude builds up cycle after cycle. The swing in the opening section is the clearest example there is.
A standard demonstration with two tuning forks. Mount two identical tuning forks on separate sounding boxes, a short distance apart.
- Strike one fork and let it sound, then stop it with your hand
- The second fork is found to be vibrating, and can be heard
- The sound waves from the first fork applied a periodic force to the second at exactly its own natural frequency, so it resonated
- Load one fork with a little wax to change its natural frequency and the effect disappears, because the two frequencies no longer match
That last step is the control that proves the explanation. Without it the demonstration only shows that sound travelled from one fork to the other; with it, the matching of frequencies is shown to be essential.
A resonance tube or air-column demonstration. Hold a vibrating tuning fork over the open end of a tube whose length can be adjusted by raising or lowering the water in it.
- At most lengths the sound is faint
- At certain particular lengths the sound becomes suddenly much louder, because the natural frequency of the air column then matches the fork's frequency
- Those lengths let the natural frequency of a column of air be measured, and hence the speed of sound
Applications of resonance, and each should be given with its reason:
- The sounding board or box of a musical instrument. A sitar, guitar, violin or tanpura has a hollow body whose air column and wooden board resonate with the strings, setting a much larger mass of air in motion and making the note far louder
- Tuning a radio or television receiver. The receiver's circuit has an adjustable natural frequency; tuning means adjusting it until it matches the frequency of the desired station, which the circuit then responds to strongly while ignoring the others
- A microwave oven. The microwaves are produced at a frequency that matches a natural frequency of the water molecules in the food, which therefore absorb the energy strongly and heat the food from within
- A wind instrument such as a flute. Blowing across the hole excites the air column, which responds strongly at its own natural frequencies; covering and uncovering the holes changes the length of the column and therefore the note
And one precaution based on resonance. Soldiers marching across a bridge are made to break step. If the rhythm of their footfall happened to match a natural frequency of the bridge, the bridge would resonate and its amplitude of vibration could build up dangerously. Breaking step makes the force irregular, so there is no single driving frequency to resonate with.
The same reason applies to a heavy machine bolted to a floor. If the machine's running speed matches a natural frequency of the floor or of a nearby panel, that part vibrates violently. The cure is to change one of the two frequencies — by altering the running speed, or by stiffening or loading the panel.
One distinction that questions test. All resonance is forced vibration, but not all forced vibration is resonance.
- A tuning fork pressed on a table forces the table to vibrate at the fork's frequency, which is almost certainly not the table's natural frequency. That is forced vibration without resonance
- A second identical fork set going by the first is vibrating at its own natural frequency. That is resonance
So resonance is the special case, and the test is whether the driving frequency equals the natural frequency of the responding body.
Why the amplitude grows so much. In ordinary forced vibrations the driving force is sometimes helping the motion and sometimes opposing it, so the energy fed in is partly cancelled. When the two frequencies match, the force is in step with the motion at every cycle, so every push adds energy and the amplitude builds up cycle after cycle. The swing in the opening section is the clearest example there is.
A standard demonstration with two tuning forks. Mount two identical tuning forks on separate sounding boxes, a short distance apart.
- Strike one fork and let it sound, then stop it with your hand
- The second fork is found to be vibrating, and can be heard
- The sound waves from the first fork applied a periodic force to the second at exactly its own natural frequency, so it resonated
- Load one fork with a little wax to change its natural frequency and the effect disappears, because the two frequencies no longer match
That last step is the control that proves the explanation. Without it the demonstration only shows that sound travelled from one fork to the other; with it, the matching of frequencies is shown to be essential.
A resonance tube or air-column demonstration. Hold a vibrating tuning fork over the open end of a tube whose length can be adjusted by raising or lowering the water in it.
- At most lengths the sound is faint
- At certain particular lengths the sound becomes suddenly much louder, because the natural frequency of the air column then matches the fork's frequency
- Those lengths let the natural frequency of a column of air be measured, and hence the speed of sound
Applications of resonance, and each should be given with its reason:
- The sounding board or box of a musical instrument. A sitar, guitar, violin or tanpura has a hollow body whose air column and wooden board resonate with the strings, setting a much larger mass of air in motion and making the note far louder
- Tuning a radio or television receiver. The receiver's circuit has an adjustable natural frequency; tuning means adjusting it until it matches the frequency of the desired station, which the circuit then responds to strongly while ignoring the others
- A microwave oven. The microwaves are produced at a frequency that matches a natural frequency of the water molecules in the food, which therefore absorb the energy strongly and heat the food from within
- A wind instrument such as a flute. Blowing across the hole excites the air column, which responds strongly at its own natural frequencies; covering and uncovering the holes changes the length of the column and therefore the note
And one precaution based on resonance. Soldiers marching across a bridge are made to break step. If the rhythm of their footfall happened to match a natural frequency of the bridge, the bridge would resonate and its amplitude of vibration could build up dangerously. Breaking step makes the force irregular, so there is no single driving frequency to resonate with.
The same reason applies to a heavy machine bolted to a floor. If the machine's running speed matches a natural frequency of the floor or of a nearby panel, that part vibrates violently. The cure is to change one of the two frequencies — by altering the running speed, or by stiffening or loading the panel.
One distinction that questions test. All resonance is forced vibration, but not all forced vibration is resonance.
- A tuning fork pressed on a table forces the table to vibrate at the fork's frequency, which is almost certainly not the table's natural frequency. That is forced vibration without resonance
- A second identical fork set going by the first is vibrating at its own natural frequency. That is resonance
So resonance is the special case, and the test is whether the driving frequency equals the natural frequency of the responding body.
How do loudness and intensity differ, and what does the decibel measure?
Intensity is a measurable physical quantity belonging to the wave; loudness is the sensation it produces in a listener's ear. Two people can hear the same intensity as different loudnesses.
Intensity. The intensity of sound at a point is the amount of sound energy passing per second per unit area held normally at that point.
- It is an objective quantity, measurable with an instrument
- Its unit is the watt per square metre
- It does not depend on the listener at all
Loudness. The loudness of a sound is the degree of sensation it produces in the ear.
- It is a subjective quantity, different for different listeners
- A person with impaired hearing perceives less loudness from the same intensity than a person with normal hearing
- It cannot be measured by an instrument, because it is not a property of the wave
What loudness depends on, which is a standard list:
- The amplitude of vibration of the source — loudness is proportional to the square of the amplitude, so doubling the amplitude makes the sound four times as loud
- The surface area of the vibrating body — a larger vibrating area sets more air in motion, which is why a tuning fork on a table is louder than one held in the air
- The density of the medium — a denser medium carries more energy for the same amplitude
- The distance from the source — the sound spreads out, so the intensity and the loudness fall as you move away
- The presence of resonant bodies nearby, which amplify the sound
- The sensitivity of the listener's ear
Notice that the first five are objective and the last is not. That is precisely why loudness is a subjective quantity — it has an objective cause and a personal outcome.
The three pairs to keep straight, which is the most examined idea in this section:
- Loudness is the subjective counterpart of intensity
- Pitch is the subjective counterpart of frequency
- Quality is the subjective counterpart of waveform
The decibel. Because the ear responds to an enormous range of intensities, the sound level is measured on a logarithmic scale whose unit is the decibel (dB).
- **The zero of the scale, dB, is the threshold of audibility — the faintest intensity a normal ear can just detect. It is a reference level, not an absence of sound
- A rise of dB corresponds to the intensity becoming ten times as great**, and a rise of dB to a hundred times
- So the scale compresses a huge range of intensities into a manageable set of numbers
Which explains something that puzzles students. A sound of dB is not "twice as intense" as one of dB — it is a thousand times as intense, because thirty decibels means three factors of ten. The decibel scale is multiplicative, and reading it as if it were additive gives wildly wrong comparisons.
Noise pollution, which follows from the same idea. Prolonged exposure to high sound levels damages hearing, and very high levels cause pain. This is why loudspeakers, horns and machinery are subject to limits, and why hearing protection is worn in noisy workplaces.
One boundary case worth stating. Because loudness depends on the distance from the source as well as on the source itself, the same sound is a different loudness in different places. So a statement about loudness is incomplete without saying where the listener is — whereas the intensity of the source is a fixed property of the source.
Intensity. The intensity of sound at a point is the amount of sound energy passing per second per unit area held normally at that point.
- It is an objective quantity, measurable with an instrument
- Its unit is the watt per square metre
- It does not depend on the listener at all
Loudness. The loudness of a sound is the degree of sensation it produces in the ear.
- It is a subjective quantity, different for different listeners
- A person with impaired hearing perceives less loudness from the same intensity than a person with normal hearing
- It cannot be measured by an instrument, because it is not a property of the wave
What loudness depends on, which is a standard list:
- The amplitude of vibration of the source — loudness is proportional to the square of the amplitude, so doubling the amplitude makes the sound four times as loud
- The surface area of the vibrating body — a larger vibrating area sets more air in motion, which is why a tuning fork on a table is louder than one held in the air
- The density of the medium — a denser medium carries more energy for the same amplitude
- The distance from the source — the sound spreads out, so the intensity and the loudness fall as you move away
- The presence of resonant bodies nearby, which amplify the sound
- The sensitivity of the listener's ear
Notice that the first five are objective and the last is not. That is precisely why loudness is a subjective quantity — it has an objective cause and a personal outcome.
The three pairs to keep straight, which is the most examined idea in this section:
- Loudness is the subjective counterpart of intensity
- Pitch is the subjective counterpart of frequency
- Quality is the subjective counterpart of waveform
The decibel. Because the ear responds to an enormous range of intensities, the sound level is measured on a logarithmic scale whose unit is the decibel (dB).
- **The zero of the scale, dB, is the threshold of audibility — the faintest intensity a normal ear can just detect. It is a reference level, not an absence of sound
- A rise of dB corresponds to the intensity becoming ten times as great**, and a rise of dB to a hundred times
- So the scale compresses a huge range of intensities into a manageable set of numbers
Which explains something that puzzles students. A sound of dB is not "twice as intense" as one of dB — it is a thousand times as intense, because thirty decibels means three factors of ten. The decibel scale is multiplicative, and reading it as if it were additive gives wildly wrong comparisons.
Noise pollution, which follows from the same idea. Prolonged exposure to high sound levels damages hearing, and very high levels cause pain. This is why loudspeakers, horns and machinery are subject to limits, and why hearing protection is worn in noisy workplaces.
One boundary case worth stating. Because loudness depends on the distance from the source as well as on the source itself, the same sound is a different loudness in different places. So a statement about loudness is incomplete without saying where the listener is — whereas the intensity of the source is a fixed property of the source.
How do pitch and quality distinguish one sound from another?
Pitch is decided by the frequency, and quality by the shape of the waveform. Together with loudness they are the three characteristics of a musical sound.
Pitch, or shrillness. Pitch is the characteristic that distinguishes a shrill sound from a flat one, and it is decided by the frequency of the vibration.
- A higher frequency gives a higher pitch, heard as a shriller note
- A lower frequency gives a lower pitch, heard as a flatter or deeper note
- Pitch is subjective; frequency is the objective quantity behind it
Everyday examples:
- A child's or a woman's voice has a higher pitch than a man's, because the vocal cords vibrate at a higher frequency
- A mosquito's buzz is high-pitched; a lion's roar is low-pitched — and the roar can be far louder while remaining lower in pitch
- Tightening a string on a sitar or a guitar raises its pitch, because the frequency of vibration increases with the tension
- A shorter string or a shorter air column gives a higher pitch
Worked example — comparing two notes. A tuning fork of frequency Hz and another of Hz are struck with the same force. Compare their pitch and their loudness.
- **The Hz fork has twice the frequency, so its pitch is higher — one octave higher, in fact
- Struck with the same force they may have similar loudness, since loudness depends on the amplitude and not on the frequency
So pitch and loudness are independent. A high-pitched sound can be faint and a low-pitched one deafening. Confusing the two — saying a shrill sound is "louder" — is the commonest error in this section.
Quality, or timbre. Quality is the characteristic that distinguishes two sounds of the same loudness and the same pitch coming from different sources, and it is decided by the waveform.
- A note from a flute and the same note from a violin are instantly recognisable as different, even at the same pitch and the same loudness
- The difference lies in the number and the relative strengths of the overtones — the higher frequencies accompanying the main note
- Those overtones change the shape of the wave, and the ear is sensitive to that shape
A pure note has a single frequency and a smooth waveform; a musical note from a real instrument contains a main frequency together with several overtones, giving a more complicated repeating shape. That shape is the sound's signature, and it is how you recognise a familiar voice on a telephone before the caller says who they are.
The distinction between a musical sound and a noise, which follows from the same idea:
- A musical sound is pleasant to hear, produced by a regular and periodic vibration, with a waveform that repeats
- A noise is unpleasant, produced by an irregular and non-periodic vibration, with no repeating waveform
- The boundary is not absolute — a sound may be musical at low loudness and become noise when extremely loud
The three characteristics summarised against their objective partners:
- Loudness depends on the amplitude — more precisely, on the square of the amplitude
- Pitch depends on the frequency
- Quality depends on the waveform, that is on the overtones present
And each pair is one subjective quantity with one objective cause, which is why the two lists correspond exactly and why the words must not be swapped. A question asking "on what does pitch depend?" wants frequency, and a question asking "what is pitch?" wants the sensation** — and the same distinction applies to all three.
Pitch, or shrillness. Pitch is the characteristic that distinguishes a shrill sound from a flat one, and it is decided by the frequency of the vibration.
- A higher frequency gives a higher pitch, heard as a shriller note
- A lower frequency gives a lower pitch, heard as a flatter or deeper note
- Pitch is subjective; frequency is the objective quantity behind it
Everyday examples:
- A child's or a woman's voice has a higher pitch than a man's, because the vocal cords vibrate at a higher frequency
- A mosquito's buzz is high-pitched; a lion's roar is low-pitched — and the roar can be far louder while remaining lower in pitch
- Tightening a string on a sitar or a guitar raises its pitch, because the frequency of vibration increases with the tension
- A shorter string or a shorter air column gives a higher pitch
Worked example — comparing two notes. A tuning fork of frequency Hz and another of Hz are struck with the same force. Compare their pitch and their loudness.
- **The Hz fork has twice the frequency, so its pitch is higher — one octave higher, in fact
- Struck with the same force they may have similar loudness, since loudness depends on the amplitude and not on the frequency
So pitch and loudness are independent. A high-pitched sound can be faint and a low-pitched one deafening. Confusing the two — saying a shrill sound is "louder" — is the commonest error in this section.
Quality, or timbre. Quality is the characteristic that distinguishes two sounds of the same loudness and the same pitch coming from different sources, and it is decided by the waveform.
- A note from a flute and the same note from a violin are instantly recognisable as different, even at the same pitch and the same loudness
- The difference lies in the number and the relative strengths of the overtones — the higher frequencies accompanying the main note
- Those overtones change the shape of the wave, and the ear is sensitive to that shape
A pure note has a single frequency and a smooth waveform; a musical note from a real instrument contains a main frequency together with several overtones, giving a more complicated repeating shape. That shape is the sound's signature, and it is how you recognise a familiar voice on a telephone before the caller says who they are.
The distinction between a musical sound and a noise, which follows from the same idea:
- A musical sound is pleasant to hear, produced by a regular and periodic vibration, with a waveform that repeats
- A noise is unpleasant, produced by an irregular and non-periodic vibration, with no repeating waveform
- The boundary is not absolute — a sound may be musical at low loudness and become noise when extremely loud
The three characteristics summarised against their objective partners:
- Loudness depends on the amplitude — more precisely, on the square of the amplitude
- Pitch depends on the frequency
- Quality depends on the waveform, that is on the overtones present
And each pair is one subjective quantity with one objective cause, which is why the two lists correspond exactly and why the words must not be swapped. A question asking "on what does pitch depend?" wants frequency, and a question asking "what is pitch?" wants the sensation** — and the same distinction applies to all three.
Exam tip
Which words does an examiner expect in a sound-characteristics answer?
Say whether each quantity is subjective or objective, and name its objective partner. Most of the marks in this part are for using the right word rather than for any calculation.
- Name the three subjective characteristics — loudness, pitch, quality — and their objective partners: intensity, frequency, waveform
- Define intensity as energy per second per unit area, with the unit watt per square metre
- Define loudness as a degree of sensation, and say it depends on the listener
- Say loudness is proportional to the square of the amplitude, so doubling the amplitude quadruples it
- Give all the factors affecting loudness — amplitude, surface area of the vibrating body, density of the medium, distance from the source, resonant bodies nearby, and the listener's ear
- **Say dB is the threshold of audibility**, and that a rise of dB means ten times the intensity
- Distinguish natural, damped and forced vibrations by frequency, amplitude and the presence of an external force, and say natural vibrations need a vacuum
- Define resonance as forced vibration with the two frequencies equal, and say the amplitude becomes very large
- Give the two-tuning-fork demonstration with its control — loading one fork with wax stops the effect
- Say a tuning fork on a table is louder but shorter-lived, and give the energy reason
The misconception to name. Pitch and loudness are independent, and a shrill sound is not a loud one. A mosquito's buzz is high-pitched and faint; a lion's roar is low-pitched and loud. Pitch is governed by frequency and loudness by amplitude, and the two can be varied separately — which is exactly what a musician does when playing the same note softly or forcefully.
A second trap. Treating the decibel scale as if it were ordinary counting. **A rise of dB is a tenfold rise in intensity, and dB is a hundredfold** — so a difference of thirty decibels is a factor of a thousand, not a factor of thirty. Any statement comparing two sound levels must use that multiplicative rule.
- Name the three subjective characteristics — loudness, pitch, quality — and their objective partners: intensity, frequency, waveform
- Define intensity as energy per second per unit area, with the unit watt per square metre
- Define loudness as a degree of sensation, and say it depends on the listener
- Say loudness is proportional to the square of the amplitude, so doubling the amplitude quadruples it
- Give all the factors affecting loudness — amplitude, surface area of the vibrating body, density of the medium, distance from the source, resonant bodies nearby, and the listener's ear
- **Say dB is the threshold of audibility**, and that a rise of dB means ten times the intensity
- Distinguish natural, damped and forced vibrations by frequency, amplitude and the presence of an external force, and say natural vibrations need a vacuum
- Define resonance as forced vibration with the two frequencies equal, and say the amplitude becomes very large
- Give the two-tuning-fork demonstration with its control — loading one fork with wax stops the effect
- Say a tuning fork on a table is louder but shorter-lived, and give the energy reason
The misconception to name. Pitch and loudness are independent, and a shrill sound is not a loud one. A mosquito's buzz is high-pitched and faint; a lion's roar is low-pitched and loud. Pitch is governed by frequency and loudness by amplitude, and the two can be varied separately — which is exactly what a musician does when playing the same note softly or forcefully.
A second trap. Treating the decibel scale as if it were ordinary counting. **A rise of dB is a tenfold rise in intensity, and dB is a hundredfold** — so a difference of thirty decibels is a factor of a thousand, not a factor of thirty. Any statement comparing two sound levels must use that multiplicative rule.
Did you know
Why does a guitar need a hollow body at all?
Stretch a wire between two nails on a solid block of wood and pluck it. You get a note, but a very faint one. Stretch the same wire over a hollow box and pluck it again and the note fills the room.
The wire is doing exactly the same thing in both cases. What has changed is how much air it manages to move.
A thin wire vibrating in air is a hopeless mover of air — it simply slices through it, disturbing very little. A guitar's belly, driven by the string through the bridge, is a broad flat surface, and a broad surface pushes on a great deal of air at once. So the string's energy reaches the room far more efficiently.
And the hollow body adds a second effect on top of that. The air inside the box has natural frequencies of its own, and at certain notes those frequencies match the string's. The air column then resonates and reinforces the note strongly — which is why some notes on an instrument sound noticeably fuller than others, and why the size and shape of the body determine the instrument's character.
That is why every acoustic instrument has a resonating body, and why the shape differs from one to the next.
- A sitar has a large gourd, giving low natural frequencies and a deep resonance
- A tabla's stretched skin over a hollow shell resonates with the drum's own vibration
- A tanpura's long hollow neck and gourd sustain the drone
- A violin's carefully carved belly and back are shaped to resonate over a wide range of notes
But the energy has to come from somewhere, and this is the honest part. Nothing about the box creates energy. The string was given a fixed amount of energy when it was plucked, and a resonating body simply lets it out faster.
Which is why a loud instrument is not a long-lasting one. Pluck a string on a solid block and the faint note lasts a long time; pluck it on a good soundboard and the loud note dies away much sooner. The same energy, spent at different rates — and that is exactly the trade-off the tuning fork on the table demonstrates in this chapter.
The same reasoning explains why a tuning fork is made of two prongs. They vibrate in opposite directions, so the fork is a poor mover of air on its own and produces a faint, very pure, long-lasting note. That is a feature, not a defect — a fork is meant to hold a steady frequency for tuning, so being inefficient at radiating sound is precisely what makes it useful. And pressing its stem on a table converts it from a reference into an instrument, at the cost of the long duration.
One last connection. A radio receiver tuning to a station and a guitar body reinforcing a note are the same physics: a system with an adjustable natural frequency, responding strongly when the driving frequency matches and weakly when it does not. In one case the driving force is a radio wave and in the other a vibrating string, but the selectivity — the reason the radio picks one station out of hundreds — is the same reason a guitar body suits some notes better than others.
The wire is doing exactly the same thing in both cases. What has changed is how much air it manages to move.
A thin wire vibrating in air is a hopeless mover of air — it simply slices through it, disturbing very little. A guitar's belly, driven by the string through the bridge, is a broad flat surface, and a broad surface pushes on a great deal of air at once. So the string's energy reaches the room far more efficiently.
And the hollow body adds a second effect on top of that. The air inside the box has natural frequencies of its own, and at certain notes those frequencies match the string's. The air column then resonates and reinforces the note strongly — which is why some notes on an instrument sound noticeably fuller than others, and why the size and shape of the body determine the instrument's character.
That is why every acoustic instrument has a resonating body, and why the shape differs from one to the next.
- A sitar has a large gourd, giving low natural frequencies and a deep resonance
- A tabla's stretched skin over a hollow shell resonates with the drum's own vibration
- A tanpura's long hollow neck and gourd sustain the drone
- A violin's carefully carved belly and back are shaped to resonate over a wide range of notes
But the energy has to come from somewhere, and this is the honest part. Nothing about the box creates energy. The string was given a fixed amount of energy when it was plucked, and a resonating body simply lets it out faster.
Which is why a loud instrument is not a long-lasting one. Pluck a string on a solid block and the faint note lasts a long time; pluck it on a good soundboard and the loud note dies away much sooner. The same energy, spent at different rates — and that is exactly the trade-off the tuning fork on the table demonstrates in this chapter.
The same reasoning explains why a tuning fork is made of two prongs. They vibrate in opposite directions, so the fork is a poor mover of air on its own and produces a faint, very pure, long-lasting note. That is a feature, not a defect — a fork is meant to hold a steady frequency for tuning, so being inefficient at radiating sound is precisely what makes it useful. And pressing its stem on a table converts it from a reference into an instrument, at the cost of the long duration.
One last connection. A radio receiver tuning to a station and a guitar body reinforcing a note are the same physics: a system with an adjustable natural frequency, responding strongly when the driving frequency matches and weakly when it does not. In one case the driving force is a radio wave and in the other a vibrating string, but the selectivity — the reason the radio picks one station out of hundreds — is the same reason a guitar body suits some notes better than others.
Exam relevance
How do vibrations and resonance prepare you for JEE and NEET?
This is foundation work for Class 11 Oscillations and Waves, both examined in JEE Main, JEE Advanced and NEET Physics.
Where the three kinds of vibration lead. Class 11 treats them quantitatively as free, damped and forced oscillations, with the damping described by a force proportional to the velocity and the amplitude falling exponentially with time. The statement here that the frequency is practically unchanged while the amplitude falls is what that treatment proves, and JEE Main sets questions on the energy of a damped oscillator.
Where resonance leads. Class 11 derives the amplitude of a forced oscillator as a function of the driving frequency, and shows that it peaks sharply when the driving frequency equals the natural frequency. The sharpness of that peak depends on the damping, which is why a lightly damped system resonates violently and a heavily damped one barely at all. JEE Main asks for the resonant frequency and NEET for the qualitative behaviour, and the same mathematics reappears in Class 12 as resonance in an alternating-current circuit — which is exactly how a radio tunes.
Where the air-column demonstration leads. Class 11 works out the natural frequencies of open and closed pipes and uses the resonance-tube experiment to measure the speed of sound. The observation here that the sound becomes suddenly louder at particular lengths is the experimental basis of that measurement, and the numerical version of it is a standard JEE Main question.
Where intensity leads. Class 11 relates the intensity of a wave to the square of its amplitude and shows that it falls as the inverse square of the distance from a point source. The factors affecting loudness that you list here are that relation in words, and the decibel scale is defined properly as a logarithm of the intensity ratio.
Where pitch and quality lead. Class 11 treats harmonics and overtones quantitatively for strings and pipes, and shows that the quality of a note is decided by which harmonics are present and how strong they are. The waveform explanation given here is exactly that result before the mathematics. The Doppler effect then makes pitch a measurable consequence of relative motion.
Where the decibel leads. It reappears in NEET in the context of noise pollution and hearing damage, and in Class 12 in the measurement of signal levels.
Question types to expect. At this level: distinguishing the three kinds of vibration, defining resonance with a demonstration, the loudness-against-intensity distinction, and the three characteristics with their objective partners. In competitive papers: damped-oscillator energy, resonant frequency, harmonics of strings and pipes, resonance-tube numericals, intensity and inverse-square falloff, and the Doppler effect.
The single trap that costs marks. Treating every forced vibration as resonance. Resonance requires the driving frequency to equal the natural frequency — a tuning fork pressed on a table forces the table at the fork's frequency, which is not the table's own, so that is forced vibration without resonance. At JEE level the same error appears as assuming maximum amplitude whenever a driving force is present.
A second trap. Confusing loudness with pitch, or intensity with frequency. Loudness comes from amplitude and pitch from frequency, and they vary independently. In competitive papers the equivalent slip is using an amplitude where an angular frequency belongs in an oscillation formula.
Board versus competitive emphasis. The ICSE paper marks the three definitions with an example each, the resonance demonstration with its control, and the subjective-objective pairing; a competitive paper marks a resonant frequency, a pipe length or an intensity ratio. The transferable habit is asking which frequency a body is actually vibrating at — its own or the driver's — because that one question separates free from forced vibration, tells you whether resonance is possible, and is the first step of every oscillation problem you will meet.
Where the three kinds of vibration lead. Class 11 treats them quantitatively as free, damped and forced oscillations, with the damping described by a force proportional to the velocity and the amplitude falling exponentially with time. The statement here that the frequency is practically unchanged while the amplitude falls is what that treatment proves, and JEE Main sets questions on the energy of a damped oscillator.
Where resonance leads. Class 11 derives the amplitude of a forced oscillator as a function of the driving frequency, and shows that it peaks sharply when the driving frequency equals the natural frequency. The sharpness of that peak depends on the damping, which is why a lightly damped system resonates violently and a heavily damped one barely at all. JEE Main asks for the resonant frequency and NEET for the qualitative behaviour, and the same mathematics reappears in Class 12 as resonance in an alternating-current circuit — which is exactly how a radio tunes.
Where the air-column demonstration leads. Class 11 works out the natural frequencies of open and closed pipes and uses the resonance-tube experiment to measure the speed of sound. The observation here that the sound becomes suddenly louder at particular lengths is the experimental basis of that measurement, and the numerical version of it is a standard JEE Main question.
Where intensity leads. Class 11 relates the intensity of a wave to the square of its amplitude and shows that it falls as the inverse square of the distance from a point source. The factors affecting loudness that you list here are that relation in words, and the decibel scale is defined properly as a logarithm of the intensity ratio.
Where pitch and quality lead. Class 11 treats harmonics and overtones quantitatively for strings and pipes, and shows that the quality of a note is decided by which harmonics are present and how strong they are. The waveform explanation given here is exactly that result before the mathematics. The Doppler effect then makes pitch a measurable consequence of relative motion.
Where the decibel leads. It reappears in NEET in the context of noise pollution and hearing damage, and in Class 12 in the measurement of signal levels.
Question types to expect. At this level: distinguishing the three kinds of vibration, defining resonance with a demonstration, the loudness-against-intensity distinction, and the three characteristics with their objective partners. In competitive papers: damped-oscillator energy, resonant frequency, harmonics of strings and pipes, resonance-tube numericals, intensity and inverse-square falloff, and the Doppler effect.
The single trap that costs marks. Treating every forced vibration as resonance. Resonance requires the driving frequency to equal the natural frequency — a tuning fork pressed on a table forces the table at the fork's frequency, which is not the table's own, so that is forced vibration without resonance. At JEE level the same error appears as assuming maximum amplitude whenever a driving force is present.
A second trap. Confusing loudness with pitch, or intensity with frequency. Loudness comes from amplitude and pitch from frequency, and they vary independently. In competitive papers the equivalent slip is using an amplitude where an angular frequency belongs in an oscillation formula.
Board versus competitive emphasis. The ICSE paper marks the three definitions with an example each, the resonance demonstration with its control, and the subjective-objective pairing; a competitive paper marks a resonant frequency, a pipe length or an intensity ratio. The transferable habit is asking which frequency a body is actually vibrating at — its own or the driver's — because that one question separates free from forced vibration, tells you whether resonance is possible, and is the first step of every oscillation problem you will meet.
Key takeaways
What must you be able to do from this part?
Three kinds of vibration, one special case and three pairs of characteristics.
- Natural or free vibrations: the body's own frequency, constant amplitude, no external periodic force — possible only in a vacuum
- Damped vibrations: practically the natural frequency but a decreasing amplitude, because energy is lost to the medium and to internal friction. Every audible vibration is damped
- Forced vibrations: the frequency of the applied periodic force, continuing while the force acts — as when a tuning fork's stem is pressed on a table
- A fork on a table is louder but dies away faster, because the same energy is spent more quickly
- Resonance is forced vibration in which the applied frequency equals the natural frequency, giving a very large amplitude
- Two identical forks demonstrate it, and loading one with wax stops the effect — which proves the frequencies must match
- A resonance tube shows sudden loudness at particular air-column lengths
- Applications: the sounding board or body of a musical instrument, tuning a radio receiver, a microwave oven heating water molecules, and the air column of a flute
- Soldiers break step on a bridge so that no single driving frequency can resonate with it
- Not all forced vibration is resonance — the frequencies must match
- Intensity is energy per second per unit area, objective, in watt per square metre; loudness is a degree of sensation, subjective, depending on the listener
- Loudness depends on the square of the amplitude, the surface area of the vibrating body, the density of the medium, the distance from the source, nearby resonant bodies, and the ear
- The decibel measures sound level, with ** dB the threshold of audibility and a rise of dB meaning ten times the intensity
- The three pairs: loudness with intensity, pitch with frequency, quality with waveform
- Pitch is shrillness and rises with frequency — a child's voice, a mosquito's buzz, a tightened or shortened string
- Pitch and loudness are independent: a mosquito is high-pitched and faint, a lion's roar low-pitched and loud
- Quality or timbre distinguishes two sounds of the same pitch and loudness from different sources, and depends on the overtones present and hence on the waveform
- A musical sound has a regular periodic waveform; a noise has an irregular one**
The best self-test needs one rubber band. Stretch it between two fingers and pluck it, then stretch it across the mouth of an open box and pluck it again — and describe in the right vocabulary which of loudness, pitch and quality changed, and why.
- Natural or free vibrations: the body's own frequency, constant amplitude, no external periodic force — possible only in a vacuum
- Damped vibrations: practically the natural frequency but a decreasing amplitude, because energy is lost to the medium and to internal friction. Every audible vibration is damped
- Forced vibrations: the frequency of the applied periodic force, continuing while the force acts — as when a tuning fork's stem is pressed on a table
- A fork on a table is louder but dies away faster, because the same energy is spent more quickly
- Resonance is forced vibration in which the applied frequency equals the natural frequency, giving a very large amplitude
- Two identical forks demonstrate it, and loading one with wax stops the effect — which proves the frequencies must match
- A resonance tube shows sudden loudness at particular air-column lengths
- Applications: the sounding board or body of a musical instrument, tuning a radio receiver, a microwave oven heating water molecules, and the air column of a flute
- Soldiers break step on a bridge so that no single driving frequency can resonate with it
- Not all forced vibration is resonance — the frequencies must match
- Intensity is energy per second per unit area, objective, in watt per square metre; loudness is a degree of sensation, subjective, depending on the listener
- Loudness depends on the square of the amplitude, the surface area of the vibrating body, the density of the medium, the distance from the source, nearby resonant bodies, and the ear
- The decibel measures sound level, with ** dB the threshold of audibility and a rise of dB meaning ten times the intensity
- The three pairs: loudness with intensity, pitch with frequency, quality with waveform
- Pitch is shrillness and rises with frequency — a child's voice, a mosquito's buzz, a tightened or shortened string
- Pitch and loudness are independent: a mosquito is high-pitched and faint, a lion's roar low-pitched and loud
- Quality or timbre distinguishes two sounds of the same pitch and loudness from different sources, and depends on the overtones present and hence on the waveform
- A musical sound has a regular periodic waveform; a noise has an irregular one**
The best self-test needs one rubber band. Stretch it between two fingers and pluck it, then stretch it across the mouth of an open box and pluck it again — and describe in the right vocabulary which of loudness, pitch and quality changed, and why.