Loudness and Pitch Are Set by Two Completely Different Things
Learn to define amplitude, wavelength, frequency and time period with their units, use the relations linking them, and explain why amplitude decides loudness while frequency decides pitch and waveform decides quality.
Why can a whisper be high and a shout be low?
Because loudness and pitch come from two entirely separate properties of the wave.
How loud a sound is depends on the amplitude — how far the vibrating body swings. How high or low it sounds depends on the frequency — how many times it swings each second.
Those two can be changed independently, which is why a whispered high note and a bellowed low note are both perfectly possible. Confusing them is the commonest mistake in this chapter. This page covers the second part of the ICSE Class 8 Physics chapter on sound: the quantities that describe a wave, the relations between them, and what each one does to what you hear.
How loud a sound is depends on the amplitude — how far the vibrating body swings. How high or low it sounds depends on the frequency — how many times it swings each second.
Those two can be changed independently, which is why a whispered high note and a bellowed low note are both perfectly possible. Confusing them is the commonest mistake in this chapter. This page covers the second part of the ICSE Class 8 Physics chapter on sound: the quantities that describe a wave, the relations between them, and what each one does to what you hear.
What are amplitude, wavelength, frequency and time period?
Four quantities describe any sound wave completely.
**Amplitude () — the maximum displacement of a vibrating particle from its rest position. It is a length, so its unit is the metre** (), often measured in millimetres for real vibrations.
**Wavelength () — the distance between two consecutive compressions, or equally between two consecutive rarefactions. It is the length of one complete wave, and its unit is the metre** ().
**Frequency () — the number of complete vibrations made in one second. Its unit is the hertz** (), where is one vibration per second. Larger units are the kilohertz, .
**Time period () — the time taken for one complete vibration. Its unit is the second** ().
How to keep frequency and time period straight. Frequency counts vibrations per second; time period counts seconds per vibration. They answer opposite questions, which is why one is the reciprocal of the other.
A fifth quantity, already met in the previous part, is the **speed ()** at which the wave travels — about in air, measured in .
The one that belongs to the medium, not the source. Amplitude, frequency and time period are decided by the vibrating source. The speed is decided almost entirely by the medium — the same note sounds at the same pitch in air and in water, but travels far faster in water. Wavelength then has to adjust, as the next section shows.
**Amplitude () — the maximum displacement of a vibrating particle from its rest position. It is a length, so its unit is the metre** (), often measured in millimetres for real vibrations.
**Wavelength () — the distance between two consecutive compressions, or equally between two consecutive rarefactions. It is the length of one complete wave, and its unit is the metre** ().
**Frequency () — the number of complete vibrations made in one second. Its unit is the hertz** (), where is one vibration per second. Larger units are the kilohertz, .
**Time period () — the time taken for one complete vibration. Its unit is the second** ().
How to keep frequency and time period straight. Frequency counts vibrations per second; time period counts seconds per vibration. They answer opposite questions, which is why one is the reciprocal of the other.
A fifth quantity, already met in the previous part, is the **speed ()** at which the wave travels — about in air, measured in .
The one that belongs to the medium, not the source. Amplitude, frequency and time period are decided by the vibrating source. The speed is decided almost entirely by the medium — the same note sounds at the same pitch in air and in water, but travels far faster in water. Wavelength then has to adjust, as the next section shows.
Formula
How are frequency, time period, speed and wavelength related?
Two relations connect all of them.
Frequency and time period are reciprocals:
Wave speed is frequency times wavelength:
Worked example 1 — from time period to frequency. A tuning fork completes one vibration in :
Worked example 2 — from frequency to time period. A source vibrates at :
Worked example 3 — finding a wavelength. The fork above sounds in air, where :
Worked example 4 — finding a frequency. A wave in air has a wavelength of :
Worked example 5 — the full chain. A body has a time period of . Find its frequency and the wavelength of the sound it makes in air.
What happens when the medium changes. Send that same note into water, where is about :
The frequency is unchanged — it is set by the source, which is still vibrating times a second. The speed rose, so the wavelength stretched to match. This is why a note keeps its pitch when it passes from air into water: pitch follows frequency, and frequency is what the medium cannot alter.
Frequency and time period are reciprocals:
Wave speed is frequency times wavelength:
Worked example 1 — from time period to frequency. A tuning fork completes one vibration in :
Worked example 2 — from frequency to time period. A source vibrates at :
Worked example 3 — finding a wavelength. The fork above sounds in air, where :
Worked example 4 — finding a frequency. A wave in air has a wavelength of :
Worked example 5 — the full chain. A body has a time period of . Find its frequency and the wavelength of the sound it makes in air.
What happens when the medium changes. Send that same note into water, where is about :
The frequency is unchanged — it is set by the source, which is still vibrating times a second. The speed rose, so the wavelength stretched to match. This is why a note keeps its pitch when it passes from air into water: pitch follows frequency, and frequency is what the medium cannot alter.
What decides how loud and how high a sound is?
Loudness follows amplitude. Pitch follows frequency. Two different properties, two different effects.
Loudness and amplitude. A larger amplitude means the vibrating body swings further, pushes more air, and carries more energy — so the sound is louder. Strike a tabla gently and it is soft; strike it hard and the same skin, vibrating the same number of times per second, gives a much louder note at the same pitch.
Loudness also falls as you move away from the source, because the energy spreads over a larger area. The sound has not changed; your share of it has. Loudness is measured in decibels ().
Pitch and frequency. A higher frequency sounds shriller or higher; a lower frequency sounds deeper or lower. A mosquito's fast wingbeat gives a high buzz; a large drum vibrating slowly gives a deep boom.
On a stringed instrument such as a sitar, pressing the string shorter makes it vibrate faster, raising the frequency and the pitch. Tightening it does the same. This is why a musician tunes by adjusting tension, not by plucking harder.
The audible range. The human ear responds roughly from to . Below the vibrations are infrasonic; above they are ultrasonic. Both are genuine sound waves that we simply cannot hear, and many animals hear well beyond our upper limit.
The test that separates the two ideas. Take a tuning fork and strike it twice, once gently and once hard. The frequency is both times, so the pitch is identical — only the loudness differs. Now take a fork and strike it gently. It is quiet and higher than the first. Amplitude and frequency have moved independently, exactly as claimed.
Loudness and amplitude. A larger amplitude means the vibrating body swings further, pushes more air, and carries more energy — so the sound is louder. Strike a tabla gently and it is soft; strike it hard and the same skin, vibrating the same number of times per second, gives a much louder note at the same pitch.
Loudness also falls as you move away from the source, because the energy spreads over a larger area. The sound has not changed; your share of it has. Loudness is measured in decibels ().
Pitch and frequency. A higher frequency sounds shriller or higher; a lower frequency sounds deeper or lower. A mosquito's fast wingbeat gives a high buzz; a large drum vibrating slowly gives a deep boom.
On a stringed instrument such as a sitar, pressing the string shorter makes it vibrate faster, raising the frequency and the pitch. Tightening it does the same. This is why a musician tunes by adjusting tension, not by plucking harder.
The audible range. The human ear responds roughly from to . Below the vibrations are infrasonic; above they are ultrasonic. Both are genuine sound waves that we simply cannot hear, and many animals hear well beyond our upper limit.
The test that separates the two ideas. Take a tuning fork and strike it twice, once gently and once hard. The frequency is both times, so the pitch is identical — only the loudness differs. Now take a fork and strike it gently. It is quiet and higher than the first. Amplitude and frequency have moved independently, exactly as claimed.
Why do a flute and a sitar playing the same note still sound different?
Because their waveforms differ. That difference is the quality, or timbre, of the sound.
Play the same note on a flute and on a sitar and both have the same frequency, so both have the same pitch. Match their volumes and both have the same loudness. Yet nobody would confuse them — and the only remaining property that can differ is the shape of the wave.
A real instrument never produces a single pure vibration. Along with the main note it produces a set of fainter, faster vibrations, and the mixture is different for every instrument. Added together they give a wave with a distinctive shape, and the ear reads that shape as the instrument's character.
So the three characteristics of a musical sound are:
- Loudness — from amplitude
- Pitch — from frequency
- Quality (timbre) — from waveform
A tuning fork comes closest to a single pure vibration, which is why its note sounds plain and characterless compared with any instrument.
Musical sound and noise. A musical sound is pleasant to hear, produced by regular and periodic vibrations that repeat the same pattern — a flute, a veena, a tuning fork. A noise is unpleasant, produced by irregular and non-periodic vibrations with no repeating pattern — a slamming door, a horn, machinery, a falling vessel.
The boundary is not only about the source. A pleasant sound becomes noise when it is too loud or unwanted — music at midnight is noise to a sleeping neighbour. And a sudden very loud sound, however musical its source, is unpleasant. So loudness and context both play a part alongside the regularity of the vibration.
Why this matters beyond the syllabus. Excessive noise causes tiredness, loss of concentration and, over long exposure, lasting damage to hearing — which is the reason horn-free zones exist around hospitals and schools.
Play the same note on a flute and on a sitar and both have the same frequency, so both have the same pitch. Match their volumes and both have the same loudness. Yet nobody would confuse them — and the only remaining property that can differ is the shape of the wave.
A real instrument never produces a single pure vibration. Along with the main note it produces a set of fainter, faster vibrations, and the mixture is different for every instrument. Added together they give a wave with a distinctive shape, and the ear reads that shape as the instrument's character.
So the three characteristics of a musical sound are:
- Loudness — from amplitude
- Pitch — from frequency
- Quality (timbre) — from waveform
A tuning fork comes closest to a single pure vibration, which is why its note sounds plain and characterless compared with any instrument.
Musical sound and noise. A musical sound is pleasant to hear, produced by regular and periodic vibrations that repeat the same pattern — a flute, a veena, a tuning fork. A noise is unpleasant, produced by irregular and non-periodic vibrations with no repeating pattern — a slamming door, a horn, machinery, a falling vessel.
The boundary is not only about the source. A pleasant sound becomes noise when it is too loud or unwanted — music at midnight is noise to a sleeping neighbour. And a sudden very loud sound, however musical its source, is unpleasant. So loudness and context both play a part alongside the regularity of the vibration.
Why this matters beyond the syllabus. Excessive noise causes tiredness, loss of concentration and, over long exposure, lasting damage to hearing — which is the reason horn-free zones exist around hospitals and schools.
Exam tip
Exam tip: never explain loudness with frequency
Pair each quality with its cause and do not swap them: loudness with amplitude, pitch with frequency, quality with waveform. Almost every lost mark in this chapter is one of those three pairs written the wrong way round.
Write units correctly: amplitude and wavelength in metres, frequency in hertz, time period in seconds, speed in metres per second, loudness in decibels.
For , convert milliseconds to seconds before dividing. A period of is , giving — using directly gives and a wrong unit.
In , state the speed you are using: in air unless the question says otherwise.
Remember what changes when the medium changes: the frequency stays the same and the wavelength adjusts. Writing that the frequency changes is a serious error, because it would mean the pitch changed.
Define wavelength as the distance between two consecutive compressions, not vaguely as the length of the wave.
And for musical sound versus noise, use the words regular and periodic against irregular and non-periodic. Pleasant and unpleasant alone is not a physics answer.
Write units correctly: amplitude and wavelength in metres, frequency in hertz, time period in seconds, speed in metres per second, loudness in decibels.
For , convert milliseconds to seconds before dividing. A period of is , giving — using directly gives and a wrong unit.
In , state the speed you are using: in air unless the question says otherwise.
Remember what changes when the medium changes: the frequency stays the same and the wavelength adjusts. Writing that the frequency changes is a serious error, because it would mean the pitch changed.
Define wavelength as the distance between two consecutive compressions, not vaguely as the length of the wave.
And for musical sound versus noise, use the words regular and periodic against irregular and non-periodic. Pleasant and unpleasant alone is not a physics answer.
Did you know
Why does a nearly empty bucket sound different as it fills?
Hold a bucket under a running tap and listen as it fills. The sound climbs steadily in pitch, and you can tell when it is nearly full without looking.
What is vibrating is the air column above the water. A tall column of air vibrates slowly, giving a low frequency and a deep sound. As water rises, the air column shortens, so it vibrates faster — the frequency climbs and the pitch rises with it.
The water is not changing and the tap is not changing. Only the length of the vibrating air column is, and that alone sets the pitch.
This is precisely how a flute works. Covering and uncovering the finger holes changes the effective length of the vibrating air column, and each length gives its own frequency and therefore its own note. A bucket under a tap is the same instrument, played badly and only once.
What is vibrating is the air column above the water. A tall column of air vibrates slowly, giving a low frequency and a deep sound. As water rises, the air column shortens, so it vibrates faster — the frequency climbs and the pitch rises with it.
The water is not changing and the tap is not changing. Only the length of the vibrating air column is, and that alone sets the pitch.
This is precisely how a flute works. Covering and uncovering the finger holes changes the effective length of the vibrating air column, and each length gives its own frequency and therefore its own note. A bucket under a tap is the same instrument, played badly and only once.
Key takeaways
Characteristics of sound: quick revision
- **Amplitude () — maximum displacement from rest, in metres.
- Wavelength () — distance between two consecutive compressions, in metres.
- Frequency () — vibrations per second, in hertz**; .
- **Time period () — time for one vibration, in seconds**.
- and : so gives , and gives .
- : at in air, gives , and gives .
- Changing the medium keeps the frequency fixed and changes the wavelength: has in air and in water.
- Loudness depends on amplitude (and falls with distance), measured in decibels.
- Pitch depends on frequency — shorter or tighter strings vibrate faster and sound higher.
- Audible range: about to ; below is infrasonic, above is ultrasonic.
- Quality (timbre) depends on waveform, which is why a flute and a sitar differ on the same note.
- Musical sound: regular, periodic vibrations. Noise: irregular, non-periodic — and an unwanted or very loud sound counts as noise whatever its source.
Work through a mixed set of and problems now, and say out loud which property causes which sensation — getting those three pairs automatic is most of this chapter.
- Wavelength () — distance between two consecutive compressions, in metres.
- Frequency () — vibrations per second, in hertz**; .
- **Time period () — time for one vibration, in seconds**.
- and : so gives , and gives .
- : at in air, gives , and gives .
- Changing the medium keeps the frequency fixed and changes the wavelength: has in air and in water.
- Loudness depends on amplitude (and falls with distance), measured in decibels.
- Pitch depends on frequency — shorter or tighter strings vibrate faster and sound higher.
- Audible range: about to ; below is infrasonic, above is ultrasonic.
- Quality (timbre) depends on waveform, which is why a flute and a sitar differ on the same note.
- Musical sound: regular, periodic vibrations. Noise: irregular, non-periodic — and an unwanted or very loud sound counts as noise whatever its source.
Work through a mixed set of and problems now, and say out loud which property causes which sensation — getting those three pairs automatic is most of this chapter.