Tap a Long Steel Railing and the Sound Arrives Twice
Learn why sound travels fastest in solids, which factors change its speed in a gas and which leave it alone, find the speed by the echo method with worked numericals, and classify frequencies as infrasonic, sonic or ultrasonic.
Why does a tap on a long steel railing arrive twice?
Put your ear against one end of a long steel railing and have a friend tap the far end once. You hear two taps.
The first arrives through the steel, the second through the air — and they arrive at different times because sound travels at very different speeds in the two materials.
Roughly:
- in air, about
- in water, about
- in steel, about
So over a railing m long, the sound through the steel takes about s and the sound through the air about s. A gap of roughly a quarter of a second — easily long enough to hear as two separate taps.
That ordering looks wrong at first. Steel is far denser than air, and a denser medium ought to be harder to disturb. The resolution is that speed depends on two properties of the medium, not one, and the other property — elasticity — differs between steel and air by far more than the density does.
This page covers the second part of the ICSE Class 9 Physics chapter on the propagation of sound waves — the speed in the three states, the factors that change it, measuring it by echo, and the range of audibility.
The first arrives through the steel, the second through the air — and they arrive at different times because sound travels at very different speeds in the two materials.
Roughly:
- in air, about
- in water, about
- in steel, about
So over a railing m long, the sound through the steel takes about s and the sound through the air about s. A gap of roughly a quarter of a second — easily long enough to hear as two separate taps.
That ordering looks wrong at first. Steel is far denser than air, and a denser medium ought to be harder to disturb. The resolution is that speed depends on two properties of the medium, not one, and the other property — elasticity — differs between steel and air by far more than the density does.
This page covers the second part of the ICSE Class 9 Physics chapter on the propagation of sound waves — the speed in the three states, the factors that change it, measuring it by echo, and the range of audibility.
Why is sound fastest in solids and slowest in gases?
Because the speed depends on how strongly the particles are coupled to each other as well as on how heavy they are — and solids win overwhelmingly on the coupling.
The two properties that decide it.
- Elasticity — how strongly a medium resists being compressed and how quickly it springs back. A greater elasticity means the disturbance is handed on faster, so the speed is greater
- Density — how much mass has to be moved. A greater density means more inertia to overcome, so the speed is smaller
So the speed rises with elasticity and falls with density:
Why solids win despite being dense. Steel is a few thousand times denser than air, which alone would make sound slower in steel. But steel's elasticity is greater than air's by a far larger factor still, and since the two appear as a ratio, the elasticity term dominates completely. The result is a speed in steel roughly fifteen times that in air.
**Worked comparison — travel times over m.**
- steel: s
- water: s
- air: s
Worked example — hearing an approaching train. Sound reaches a listener through the rail before it reaches them through the air, which is why an ear to the track gives earlier warning than listening in the ordinary way.
Everyday evidence.
- Whales and dolphins communicate over long distances in water, which carries sound both faster and further than air
- A thread telephone — two cups joined by a taut string — works because the string carries the vibration well, and goes silent the moment the string slackens
- Putting an ear to a table makes a light scratch at the far end clearly audible when it is inaudible through the air
Density alone explains nothing, and this is where most wrong answers come from. "Solids are denser, so sound travels faster" gets the right conclusion from the wrong reason — density on its own would make it slower. The correct answer must name elasticity as the dominant factor and say that it outweighs the greater density.
The same ratio explains an oddity among gases. Sound travels faster in hydrogen than in oxygen, because hydrogen is far less dense while their elastic properties are comparable. So within one state of matter, density is the factor that varies most, and between states it is elasticity — which is why the two comparisons need different explanations.
The two properties that decide it.
- Elasticity — how strongly a medium resists being compressed and how quickly it springs back. A greater elasticity means the disturbance is handed on faster, so the speed is greater
- Density — how much mass has to be moved. A greater density means more inertia to overcome, so the speed is smaller
So the speed rises with elasticity and falls with density:
Why solids win despite being dense. Steel is a few thousand times denser than air, which alone would make sound slower in steel. But steel's elasticity is greater than air's by a far larger factor still, and since the two appear as a ratio, the elasticity term dominates completely. The result is a speed in steel roughly fifteen times that in air.
**Worked comparison — travel times over m.**
- steel: s
- water: s
- air: s
Worked example — hearing an approaching train. Sound reaches a listener through the rail before it reaches them through the air, which is why an ear to the track gives earlier warning than listening in the ordinary way.
Everyday evidence.
- Whales and dolphins communicate over long distances in water, which carries sound both faster and further than air
- A thread telephone — two cups joined by a taut string — works because the string carries the vibration well, and goes silent the moment the string slackens
- Putting an ear to a table makes a light scratch at the far end clearly audible when it is inaudible through the air
Density alone explains nothing, and this is where most wrong answers come from. "Solids are denser, so sound travels faster" gets the right conclusion from the wrong reason — density on its own would make it slower. The correct answer must name elasticity as the dominant factor and say that it outweighs the greater density.
The same ratio explains an oddity among gases. Sound travels faster in hydrogen than in oxygen, because hydrogen is far less dense while their elastic properties are comparable. So within one state of matter, density is the factor that varies most, and between states it is elasticity — which is why the two comparisons need different explanations.
What changes the speed of sound in air, and what does not?
Temperature, humidity and wind change it; pressure, frequency and amplitude do not. Knowing which list an item belongs to is most of what this objective asks.
Factors that DO affect the speed.
Temperature. The speed increases as the air gets warmer, because the molecules move faster and pass the disturbance on more quickly. In terms of absolute temperature,
with in kelvin. So sound travels faster on a hot afternoon than on a cold night.
Worked example. Air is warmed from to . In kelvin that is K to K, so the speed changes by a factor of
about a per cent increase. Note that kelvin is compulsory here — using would give a factor of over two, which is badly wrong.
Humidity. The speed increases with humidity. Water vapour is less dense than the dry air it displaces, so moist air is lighter than dry air at the same temperature and pressure — and a lower density means a higher speed. That is why sound carries better on a damp day.
Wind. Wind does not change the speed through the air, but it adds its own component to the speed measured relative to the ground. Sound travelling with the wind arrives faster; against it, slower. Only the component along the direction of travel matters.
Factors that do NOT affect the speed.
Pressure, at constant temperature. This is the surprising one. Increasing the pressure of a gas increases its density in the same proportion, so the ratio is unchanged and the speed stays the same. So sound travels at the same speed at the top of a building as at its base, provided the temperature is the same.
Frequency and wavelength. A high note and a low note travel at exactly the same speed. From , a change in is matched by an opposite change in and the product is unaltered.
Amplitude, and therefore loudness. A shout and a whisper of the same note travel together.
The frequency point has a consequence you can hear. An orchestra playing a chord reaches the back of a hall with all its notes still together. If high frequencies travelled faster than low ones, music would arrive smeared and out of order, and a distant band would sound like nonsense. That everything stays in step is direct evidence that the speed is independent of frequency.
Pressure and temperature are easy to confuse because both describe the state of a gas. Raising the temperature raises the speed; raising the pressure alone does not. The reason is that pressure and density rise together while temperature raises the molecular speeds without adding molecules — and a question naming both is testing exactly that separation.
Factors that DO affect the speed.
Temperature. The speed increases as the air gets warmer, because the molecules move faster and pass the disturbance on more quickly. In terms of absolute temperature,
with in kelvin. So sound travels faster on a hot afternoon than on a cold night.
Worked example. Air is warmed from to . In kelvin that is K to K, so the speed changes by a factor of
about a per cent increase. Note that kelvin is compulsory here — using would give a factor of over two, which is badly wrong.
Humidity. The speed increases with humidity. Water vapour is less dense than the dry air it displaces, so moist air is lighter than dry air at the same temperature and pressure — and a lower density means a higher speed. That is why sound carries better on a damp day.
Wind. Wind does not change the speed through the air, but it adds its own component to the speed measured relative to the ground. Sound travelling with the wind arrives faster; against it, slower. Only the component along the direction of travel matters.
Factors that do NOT affect the speed.
Pressure, at constant temperature. This is the surprising one. Increasing the pressure of a gas increases its density in the same proportion, so the ratio is unchanged and the speed stays the same. So sound travels at the same speed at the top of a building as at its base, provided the temperature is the same.
Frequency and wavelength. A high note and a low note travel at exactly the same speed. From , a change in is matched by an opposite change in and the product is unaltered.
Amplitude, and therefore loudness. A shout and a whisper of the same note travel together.
The frequency point has a consequence you can hear. An orchestra playing a chord reaches the back of a hall with all its notes still together. If high frequencies travelled faster than low ones, music would arrive smeared and out of order, and a distant band would sound like nonsense. That everything stays in step is direct evidence that the speed is independent of frequency.
Pressure and temperature are easy to confuse because both describe the state of a gas. Raising the temperature raises the speed; raising the pressure alone does not. The reason is that pressure and density rise together while temperature raises the molecular speeds without adding molecules — and a question naming both is testing exactly that separation.
Formula
How do you measure the speed of sound and use it in numericals?
Send a sound to a distant wall, time the echo, and remember that the sound covered the distance twice.
where is the distance to the reflecting surface and the time for the echo to return.
The experiment. Stand a measured distance from a large flat wall or a cliff, clap sharply, and time the interval until the echo is heard. The factor of is the whole point — the sound travelled to the wall and back.
A better version. Clap repeatedly, adjusting the rhythm until each echo arrives exactly as the next clap is made. Count how many claps fit into a measured time. If claps take s, the interval is s, so with m,
Timing many intervals rather than one spreads the reaction-time error over all of them, which is the same reasoning as timing twenty swings of a pendulum.
Worked example 1. A person claps m from a wall and hears the echo after s:
Worked example 2. A clap m from a cliff returns after s:
Worked example 3 — finding the distance. An echo returns after s with :
Worked example 4 — thunder and lightning. Thunder is heard s after the flash is seen. Light arrives effectively instantly, so the sound alone travelled the distance once:
**No factor of here — there is no reflection. Deciding whether the journey was one way or two is the first step of every one of these problems.
Worked example 5 — sonar depth sounding.** A ship sends a pulse straight down and receives it back after s. Sound travels at about in sea water:
Worked example 6 — the minimum distance for a distinct echo. The ear can separate two sounds only if they arrive at least about s apart. For the echo to be heard as separate from the original clap,
**So a wall nearer than about m gives no distinct echo — the reflection blends into the original sound. That is why an echo is heard in a large hall or a valley and not in a small room.
Halving the is where marks are lost.** The formula gives directly, and a question asking for the distance to the wall needs that halved. **Writing as its own line before dividing** makes the step visible and prevents the distance from coming out twice too large.
where is the distance to the reflecting surface and the time for the echo to return.
The experiment. Stand a measured distance from a large flat wall or a cliff, clap sharply, and time the interval until the echo is heard. The factor of is the whole point — the sound travelled to the wall and back.
A better version. Clap repeatedly, adjusting the rhythm until each echo arrives exactly as the next clap is made. Count how many claps fit into a measured time. If claps take s, the interval is s, so with m,
Timing many intervals rather than one spreads the reaction-time error over all of them, which is the same reasoning as timing twenty swings of a pendulum.
Worked example 1. A person claps m from a wall and hears the echo after s:
Worked example 2. A clap m from a cliff returns after s:
Worked example 3 — finding the distance. An echo returns after s with :
Worked example 4 — thunder and lightning. Thunder is heard s after the flash is seen. Light arrives effectively instantly, so the sound alone travelled the distance once:
**No factor of here — there is no reflection. Deciding whether the journey was one way or two is the first step of every one of these problems.
Worked example 5 — sonar depth sounding.** A ship sends a pulse straight down and receives it back after s. Sound travels at about in sea water:
Worked example 6 — the minimum distance for a distinct echo. The ear can separate two sounds only if they arrive at least about s apart. For the echo to be heard as separate from the original clap,
**So a wall nearer than about m gives no distinct echo — the reflection blends into the original sound. That is why an echo is heard in a large hall or a valley and not in a small room.
Halving the is where marks are lost.** The formula gives directly, and a question asking for the distance to the wall needs that halved. **Writing as its own line before dividing** makes the step visible and prevents the distance from coming out twice too large.
What counts as infrasonic, sonic and ultrasonic?
**The human ear hears from about Hz to about Hz**, and the frequencies on either side get their own names.
- Infrasonic — **below Hz. Inaudible to humans
- Sonic or audible** — from Hz to Hz
- Ultrasonic — **above Hz. Also inaudible to humans
Worked classification.**
- Hz — infrasonic
- Hz — infrasonic
- Hz — audible, at the lower boundary
- Hz — audible
- Hz — audible
- Hz — ultrasonic
- Hz — ultrasonic
Sources of infrasonic sound: earthquakes and volcanic tremors, the low rumble an elephant uses to communicate over long distances, whale calls, a slowly swinging pendulum, a vibrating simple pendulum in a laboratory.
Sources of ultrasonic sound: bats, which navigate by it, dolphins, some moths and rodents, a dog whistle, and quartz crystals driven electrically in a laboratory.
Two practical uses of ultrasound.
Medical imaging (ultrasonography). A probe sends ultrasonic pulses into the body and records the echoes from the boundaries between different tissues. The pattern of return times is assembled into an image, used to examine the abdomen, the heart — where it is called echocardiography — and a developing foetus. It uses no ionising radiation, which is why it is preferred for repeated examinations.
Sonar. A ship or submarine sends a pulse and times its return, as in worked example 5 of the previous section, to find the depth of the sea bed, to locate submarines, shoals of fish, submerged rocks and wrecks.
Other uses worth knowing.
- Breaking kidney stones into fragments small enough to pass out naturally
- Cleaning delicate parts — spiral tubes, watch mechanisms, jewellery — by vibrating the liquid they sit in, which dislodges dirt from corners a brush cannot reach
- Detecting flaws in metal castings and welds: ultrasound passing through is reflected by an internal crack, revealing a defect without cutting the object open
- Welding plastics and drilling fine holes
Why ultrasound rather than audible sound for all this. Its wavelength is short, since and is large. A short wavelength can be sent out as a narrow beam instead of spreading in all directions, and it can detect small objects — a wave cannot resolve anything much smaller than its own wavelength.
Worked example. In sea water at about , a Hz pulse has
while an audible Hz sound would have m. A hundred times shorter, so a hundred times finer detail — and that is the whole reason ultrasound is the tool of choice.
The audible range shrinks with age and varies between people. The upper limit falls as a person gets older, which is why children can often hear high-pitched sounds that adults cannot. **So Hz to kHz is a standard range for a healthy young ear**, not a fixed property of every human, and the boundaries are conventional round numbers.
- Infrasonic — **below Hz. Inaudible to humans
- Sonic or audible** — from Hz to Hz
- Ultrasonic — **above Hz. Also inaudible to humans
Worked classification.**
- Hz — infrasonic
- Hz — infrasonic
- Hz — audible, at the lower boundary
- Hz — audible
- Hz — audible
- Hz — ultrasonic
- Hz — ultrasonic
Sources of infrasonic sound: earthquakes and volcanic tremors, the low rumble an elephant uses to communicate over long distances, whale calls, a slowly swinging pendulum, a vibrating simple pendulum in a laboratory.
Sources of ultrasonic sound: bats, which navigate by it, dolphins, some moths and rodents, a dog whistle, and quartz crystals driven electrically in a laboratory.
Two practical uses of ultrasound.
Medical imaging (ultrasonography). A probe sends ultrasonic pulses into the body and records the echoes from the boundaries between different tissues. The pattern of return times is assembled into an image, used to examine the abdomen, the heart — where it is called echocardiography — and a developing foetus. It uses no ionising radiation, which is why it is preferred for repeated examinations.
Sonar. A ship or submarine sends a pulse and times its return, as in worked example 5 of the previous section, to find the depth of the sea bed, to locate submarines, shoals of fish, submerged rocks and wrecks.
Other uses worth knowing.
- Breaking kidney stones into fragments small enough to pass out naturally
- Cleaning delicate parts — spiral tubes, watch mechanisms, jewellery — by vibrating the liquid they sit in, which dislodges dirt from corners a brush cannot reach
- Detecting flaws in metal castings and welds: ultrasound passing through is reflected by an internal crack, revealing a defect without cutting the object open
- Welding plastics and drilling fine holes
Why ultrasound rather than audible sound for all this. Its wavelength is short, since and is large. A short wavelength can be sent out as a narrow beam instead of spreading in all directions, and it can detect small objects — a wave cannot resolve anything much smaller than its own wavelength.
Worked example. In sea water at about , a Hz pulse has
while an audible Hz sound would have m. A hundred times shorter, so a hundred times finer detail — and that is the whole reason ultrasound is the tool of choice.
The audible range shrinks with age and varies between people. The upper limit falls as a person gets older, which is why children can often hear high-pitched sounds that adults cannot. **So Hz to kHz is a standard range for a healthy young ear**, not a fixed property of every human, and the boundaries are conventional round numbers.
Exam tip
Exam tip: decide whether the journey is one way or two
Ask first whether the sound reflected. An echo means ; thunder after lightning means with no factor of two.
**Write as its own line before halving — that is where the distance goes wrong.
Take in air and about in water unless told otherwise, and say which you used.
Quote the order** and give elasticity as the dominant reason. Never explain it by density alone — density alone would make solids slower.
Two lists, learnt as lists. Affect the speed: temperature, humidity, wind. Do not affect it: pressure, frequency, wavelength, amplitude.
For pressure, give the reason — density rises with pressure in the same proportion, so the ratio is unchanged.
**Use kelvin for **: to is K to K, a factor of .
Humidity increases the speed because water vapour is less dense than dry air.
**Range of audibility is Hz to Hz — below is infrasonic, above is ultrasonic.
Minimum distance for a distinct echo is about m**, from .
And say why ultrasound is used — its short wavelength gives a narrow beam and detects small objects.
**Write as its own line before halving — that is where the distance goes wrong.
Take in air and about in water unless told otherwise, and say which you used.
Quote the order** and give elasticity as the dominant reason. Never explain it by density alone — density alone would make solids slower.
Two lists, learnt as lists. Affect the speed: temperature, humidity, wind. Do not affect it: pressure, frequency, wavelength, amplitude.
For pressure, give the reason — density rises with pressure in the same proportion, so the ratio is unchanged.
**Use kelvin for **: to is K to K, a factor of .
Humidity increases the speed because water vapour is less dense than dry air.
**Range of audibility is Hz to Hz — below is infrasonic, above is ultrasonic.
Minimum distance for a distinct echo is about m**, from .
And say why ultrasound is used — its short wavelength gives a narrow beam and detects small objects.
Did you know
Why a bat can hunt a mosquito in the dark and you could not
A bat flies in complete darkness and catches an insect a few millimetres across. It does it by sending out ultrasonic squeaks and listening for the echoes, and the reason it works is a matter of wavelength.
A wave cannot show you anything much smaller than its own wavelength. Try to feel the shape of a small key by pushing a beach ball over it and you learn nothing — the probe is too coarse. Use a fingertip and the shape is obvious.
So put numbers on the bat's problem. Take the speed of sound in air as . A bat's call at around Hz has
A few millimetres — comparable with the insect, so the echo carries real information about it.
Now try it with a sound a human could make. A shout at Hz has
Sixty-eight centimetres. A mosquito is utterly invisible to a wave that long; it would not disturb the returning sound in any detectable way.
That is the entire difference. The bat is not louder or cleverer — it is using a finer probe, and the fineness comes from the high frequency.
The same arithmetic sets the limit on a medical scan. Higher-frequency ultrasound shows finer detail, which is why a scan of something shallow uses a higher frequency than a scan of something deep — the shorter wave shows more and also gets absorbed sooner, so there is a trade between detail and depth.
And it is why sonar finds a submarine but not a fishing line, and why detecting a hairline crack in a casting needs a higher frequency than finding a large cavity. **One relation, , decides what every echo can and cannot see.**
A wave cannot show you anything much smaller than its own wavelength. Try to feel the shape of a small key by pushing a beach ball over it and you learn nothing — the probe is too coarse. Use a fingertip and the shape is obvious.
So put numbers on the bat's problem. Take the speed of sound in air as . A bat's call at around Hz has
A few millimetres — comparable with the insect, so the echo carries real information about it.
Now try it with a sound a human could make. A shout at Hz has
Sixty-eight centimetres. A mosquito is utterly invisible to a wave that long; it would not disturb the returning sound in any detectable way.
That is the entire difference. The bat is not louder or cleverer — it is using a finer probe, and the fineness comes from the high frequency.
The same arithmetic sets the limit on a medical scan. Higher-frequency ultrasound shows finer detail, which is why a scan of something shallow uses a higher frequency than a scan of something deep — the shorter wave shows more and also gets absorbed sooner, so there is a trade between detail and depth.
And it is why sonar finds a submarine but not a fishing line, and why detecting a hairline crack in a casting needs a higher frequency than finding a large cavity. **One relation, , decides what every echo can and cannot see.**
Exam relevance
How is the speed of sound tested in JEE Main and NEET?
Because the speed formula is derived in Class 11 and the factors list becomes an algebraic result, and echo numericals persist unchanged.
This is the foundation for Class 11 Physics Waves, examined in JEE Main and NEET. The qualitative statement becomes the exact expression
with the ratio of specific heats — and every statement on this page falls out of it. Pressure appears in that formula, and yet pressure does not affect the speed, because is fixed at constant temperature. Combining it with the gas equation gives
which shows the speed depending on the absolute temperature and on the molar mass and on nothing else — so is proved, and so is the hydrogen-against-oxygen comparison from the second section. Numericals using this formula are recurring JEE Main material.
The independence of pressure is a standard assertion-reason item in both papers, and the expected reason is exactly the one given here: pressure and density rise together.
Echo numericals continue almost unchanged. Class 11 adds reverberation time and the Doppler effect, where the observed frequency changes because the source or observer moves — while the speed stays fixed by the medium. Keeping those two apart is what the factor list on this page makes possible, and it is where students most often go wrong in Doppler questions.
Sonar and ranging are examined as applications, and the factor-of-two question is the same one.
The wavelength-and-resolution argument from the previous section is the qualitative form of a result used throughout Class 12 Wave Optics: the smallest detail an instrument can resolve is set by the wavelength. That is why an electron microscope beats a light microscope, and why ultrasound frequency is chosen by the detail required.
For NEET Biology, the ear's audible range, the classification of frequencies, and the medical applications of ultrasound appear in the sense-organs and human-health chapters. Ultrasonography is examined as a diagnostic technique, and the point that it uses no ionising radiation is the examinable contrast with X-rays.
What the questions look like. For board work, expect compare the speed in the three states with the elasticity reason, two lists of factors, describe the echo method, numericals on echoes, thunder and sonar, state the range of audibility, classify given frequencies, and two uses of ultrasound with a reason. For JEE Main and NEET, expect the gas speed formula, temperature dependence, the Doppler effect, and resolution arguments.
How board and competitive emphasis differ. A board paper rewards the two lists learnt correctly and the reason for pressure having no effect. A competitive paper assumes the formula and tests whether and are applied with the right units — kelvin and molar mass.
The single trap that costs the most marks. Forgetting whether the sound made a round trip. An echo needs , and thunder after lightning needs , and using the wrong one gives an answer exactly twice or half the correct value — a plausible-looking number every time. The defence is to write one sentence before any arithmetic: the sound reflected, so it covered the distance twice — or there was no reflection, so it covered it once.
This is the foundation for Class 11 Physics Waves, examined in JEE Main and NEET. The qualitative statement becomes the exact expression
with the ratio of specific heats — and every statement on this page falls out of it. Pressure appears in that formula, and yet pressure does not affect the speed, because is fixed at constant temperature. Combining it with the gas equation gives
which shows the speed depending on the absolute temperature and on the molar mass and on nothing else — so is proved, and so is the hydrogen-against-oxygen comparison from the second section. Numericals using this formula are recurring JEE Main material.
The independence of pressure is a standard assertion-reason item in both papers, and the expected reason is exactly the one given here: pressure and density rise together.
Echo numericals continue almost unchanged. Class 11 adds reverberation time and the Doppler effect, where the observed frequency changes because the source or observer moves — while the speed stays fixed by the medium. Keeping those two apart is what the factor list on this page makes possible, and it is where students most often go wrong in Doppler questions.
Sonar and ranging are examined as applications, and the factor-of-two question is the same one.
The wavelength-and-resolution argument from the previous section is the qualitative form of a result used throughout Class 12 Wave Optics: the smallest detail an instrument can resolve is set by the wavelength. That is why an electron microscope beats a light microscope, and why ultrasound frequency is chosen by the detail required.
For NEET Biology, the ear's audible range, the classification of frequencies, and the medical applications of ultrasound appear in the sense-organs and human-health chapters. Ultrasonography is examined as a diagnostic technique, and the point that it uses no ionising radiation is the examinable contrast with X-rays.
What the questions look like. For board work, expect compare the speed in the three states with the elasticity reason, two lists of factors, describe the echo method, numericals on echoes, thunder and sonar, state the range of audibility, classify given frequencies, and two uses of ultrasound with a reason. For JEE Main and NEET, expect the gas speed formula, temperature dependence, the Doppler effect, and resolution arguments.
How board and competitive emphasis differ. A board paper rewards the two lists learnt correctly and the reason for pressure having no effect. A competitive paper assumes the formula and tests whether and are applied with the right units — kelvin and molar mass.
The single trap that costs the most marks. Forgetting whether the sound made a round trip. An echo needs , and thunder after lightning needs , and using the wrong one gives an answer exactly twice or half the correct value — a plausible-looking number every time. The defence is to write one sentence before any arithmetic: the sound reflected, so it covered the distance twice — or there was no reflection, so it covered it once.
Key takeaways
Speed of sound, its factors and the audible range: quick revision
- Speed order: solids > liquids > gases. About in steel, in water, in air.
- Over m: steel takes s, water s, air s — which is why a tapped railing is heard twice.
- ** — greater elasticity raises the speed, greater density lowers it.
- Solids win because their elasticity is greater by far more than their density is — density alone would make them slower, so never explain it by density.
- Within gases, density varies most: sound is faster in hydrogen than in oxygen.
- Factors that AFFECT the speed in a gas: temperature** ( in kelvin), humidity (moist air is less dense, so faster), wind (adds its component relative to the ground).
- to is K to K, a factor of — kelvin is compulsory.
- Factors that do NOT affect it: pressure (density rises with it, so the ratio is unchanged), frequency, wavelength and amplitude.
- All notes of a chord arrive together, which is direct evidence that speed is independent of frequency.
- Echo method: , because the sound travels to the wall and back.
- m with s gives ; m with s gives ; claps in s at m gives .
- An echo after s gives m.
- **Thunder s after lightning gives m — no factor of two, since nothing reflected.
- Sonar**: a pulse returning in s at gives a depth of m.
- **Minimum distance for a distinct echo is about m**, from .
- **Range of audibility: Hz to Hz. Below is infrasonic, above is ultrasonic**.
- Hz and Hz are infrasonic; Hz, Hz and Hz are audible; Hz and Hz are ultrasonic.
- Infrasonic sources: earthquakes, elephants, whales, a swinging pendulum. Ultrasonic sources: bats, dolphins, a dog whistle.
- Uses of ultrasound: ultrasonography and echocardiography, sonar, breaking kidney stones, cleaning delicate parts, detecting flaws in castings, welding plastics.
- Ultrasound is used because its wavelength is short — a narrow beam and fine detail. At Hz in water cm against m for Hz.
- The upper limit of hearing falls with age, so kHz describes a healthy young ear.
Stand a measured distance from a big wall, clap, and time the echo with a phone stopwatch — then work out your own value for the speed of sound.
- Over m: steel takes s, water s, air s — which is why a tapped railing is heard twice.
- ** — greater elasticity raises the speed, greater density lowers it.
- Solids win because their elasticity is greater by far more than their density is — density alone would make them slower, so never explain it by density.
- Within gases, density varies most: sound is faster in hydrogen than in oxygen.
- Factors that AFFECT the speed in a gas: temperature** ( in kelvin), humidity (moist air is less dense, so faster), wind (adds its component relative to the ground).
- to is K to K, a factor of — kelvin is compulsory.
- Factors that do NOT affect it: pressure (density rises with it, so the ratio is unchanged), frequency, wavelength and amplitude.
- All notes of a chord arrive together, which is direct evidence that speed is independent of frequency.
- Echo method: , because the sound travels to the wall and back.
- m with s gives ; m with s gives ; claps in s at m gives .
- An echo after s gives m.
- **Thunder s after lightning gives m — no factor of two, since nothing reflected.
- Sonar**: a pulse returning in s at gives a depth of m.
- **Minimum distance for a distinct echo is about m**, from .
- **Range of audibility: Hz to Hz. Below is infrasonic, above is ultrasonic**.
- Hz and Hz are infrasonic; Hz, Hz and Hz are audible; Hz and Hz are ultrasonic.
- Infrasonic sources: earthquakes, elephants, whales, a swinging pendulum. Ultrasonic sources: bats, dolphins, a dog whistle.
- Uses of ultrasound: ultrasonography and echocardiography, sonar, breaking kidney stones, cleaning delicate parts, detecting flaws in castings, welding plastics.
- Ultrasound is used because its wavelength is short — a narrow beam and fine detail. At Hz in water cm against m for Hz.
- The upper limit of hearing falls with age, so kHz describes a healthy young ear.
Stand a measured distance from a big wall, clap, and time the echo with a phone stopwatch — then work out your own value for the speed of sound.