Propagation of Sound Waves ICSE Class 9: Waves, Speed of Sound and V = fλ

What Propagation of Sound Waves is about

Weightage: CISCE publishes no chapter weightage and no question-paper layout for ICSE Class 9 Physics. Class IX is examined by your school: one 80-mark paper of 2 hours plus 20 marks of internal assessment. Propagation of Sound Waves is in the 7. Sound (i) part of the 2028 syllabus.Source: CISCE ICSE 2028 Physics syllabus, Class IX

Key concepts

Wave motion: transverse and longitudinal

Transverse wave: particles vibrate perpendicular to the direction of travel. It has crests and troughs. Examples: waves on a stretched string, ripples on water.

Longitudinal wave: particles vibrate along (parallel to) the direction of travel. It has compressions (particles crowded, high pressure) and rarefactions (particles spread out, low pressure). Examples: sound in air, waves along a slinky pushed to and fro.

Comparison:

• vibration direction: perpendicular vs parallel;
• shape: crests and troughs vs compressions and rarefactions;
• media: transverse mechanical waves need a medium that resists change of shape (solids, or the surface of liquids); longitudinal waves travel through solids, liquids and gases.

Worked example

A slinky is moved up and down at one end, and then pushed in and out along its length. Name the type of wave in each case.

Try it first, then show the solutionSolution

1. Up and down: coils move perpendicular to the wave's travel: transverse.
2. In and out: coils move along the direction of travel: longitudinal.

Answer: Transverse; longitudinal

Sound is a longitudinal mechanical wave

Sound is produced by vibrating bodies (a tuning fork, vocal cords, a drum skin). A vibrating prong pushes the nearby air layer forward, making a compression; as it moves back, it leaves a rarefaction. These pass outward through the air as a series of compressions and rarefactions.

So sound in air is a longitudinal wave. Because it depends on particles passing on their vibration, it is a mechanical wave and needs a material medium.

Worked example

The distance between a compression and the next rarefaction of a sound wave is 0.85 m. Find the wavelength.

Try it first, then show the solutionSolution

1. Wavelength = distance between two consecutive compressions.
2. A compression and the next rarefaction are half a wavelength apart.
3. $\lambda =2\times 0.85=1.7$ m.

Answer: 1.7 m

Sound needs a medium (bell-jar experiment)

An electric bell is hung inside a glass bell jar connected to a vacuum pump.
1. With air in the jar, the bell is heard clearly.
2. As air is pumped out, the sound becomes fainter, though the hammer is still seen striking the gong.
3. With nearly all air removed, almost no sound is heard.
4. When air is let back in, the sound returns.

Conclusion: sound needs a material medium; it cannot travel through a vacuum. Light can (we still see the bell). This is why astronauts on the Moon talk by radio.

Worked example

In the bell-jar experiment, why can you still see the hammer striking the gong when you can no longer hear it?

Try it first, then show the solutionSolution

1. Light is an electromagnetic wave and travels through a vacuum.
2. Sound is a mechanical wave and needs a medium, which has been removed.

Answer: Light crosses a vacuum; sound cannot.

Frequency, wavelength, time period and V = fλ

• Amplitude: the maximum displacement of a particle from its mean position.
• Time period $T$: time for one complete vibration (s).
• Frequency $f$: number of vibrations per second; unit hertz (Hz). $f=\frac{1}{T}$.
• Wavelength $\lambda$: distance travelled by the wave during one vibration of a particle; the distance between two consecutive compressions (or crests). Unit: m.
• Wave velocity $V$: distance travelled by the wave per second.

In one time period the wave travels one wavelength, so $V=\frac{\lambda }{T}=f\lambda$.

When sound passes from one medium into another, its frequency stays the same (set by the source); its speed and wavelength change.

Worked example

A tuning fork of frequency 256 Hz produces sound of wavelength 1.3 m in air. Find the speed of sound and the time period.

Try it first, then show the solutionSolution

1. $V=f\lambda =256\times 1.3=332.8$ m s⁻¹.
2. $T=\frac{1}{256}\approx 0.0039$ s.

Answer: 332.8 m s⁻¹; ≈ 0.0039 s

Speed of sound in different media and factors

Sound travels fastest in solids, slower in liquids and slowest in gases (typical values: steel about 5000 m s⁻¹, water about 1500 m s⁻¹, air about 340 m s⁻¹ at room temperature). Particles are more tightly bound in solids, so the disturbance is passed on more quickly.

Factors affecting the speed of sound in a gas:

• Temperature: speed increases as temperature rises.
• Humidity: speed increases with humidity (moist air is less dense).
• Nature (density and elasticity) of the medium.
• Pressure has no effect if the temperature is constant.
• Amplitude, frequency and wavelength do not change the speed in a given medium.

Worked example

A 500 Hz sound passes from air (340 m s⁻¹) into water (1500 m s⁻¹). Find its wavelength in each medium.

Try it first, then show the solutionSolution

1. Frequency stays 500 Hz.
2. Air: $\lambda =\frac{340}{500}=0.68$ m.
3. Water: $\lambda =\frac{1500}{500}=3$ m.

Answer: 0.68 m in air; 3 m in water

Sound compared with light: thunder and lightning

Light travels at about $3\times 10^8$ m s⁻¹, nearly a million times faster than sound in air (about 340 m s⁻¹).

Consequences:

• Lightning is seen before thunder is heard, though both are produced together. Light reaches us almost instantly; sound takes a noticeable time.
• Distance of the lightning $\approx$ speed of sound × time gap.
• At a sports meet, the smoke of the starter's gun is seen before the bang is heard far away.
• Sound needs a medium; light does not.

Worked example

Thunder is heard 3 s after a flash of lightning is seen. How far away is the storm? (Speed of sound 340 m s⁻¹.)

Try it first, then show the solutionSolution

1. The light's travel time is negligible.
2. Distance $=340\times 3=1020$ m.

Answer: About 1.02 km

Physics in real life: Propagation of Sound Waves

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Speed of Sound in Different Media, Factors and Thunder-and-Lightning Problems
• Wave Motion, Longitudinal Sound Waves and V = fλ

Propagation of Sound Waves formula sheet

Wave equation

$V=f\lambda$

m s⁻¹ = Hz × m.

Frequency and period

$f=\frac{1}{T}$

Hz = s⁻¹.

Speed from period

$V=\frac{\lambda }{T}$

One wavelength per period.

Distance

$d=V\times t$

Thunder: t = gap after the flash.

Compression to rarefaction

$\frac{\lambda }{2}$

Two compressions: λ apart.

Propagation of Sound Waves: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Propagation of Sound Waves

The question patterns to expect, and the method that works for each.

Tricks to remember Propagation of Sound Waves

Short memory aids. Say each one aloud once, then use it on a question the same day.

• T for 'tilted' vibration

  Transverse: particles move at right angles (like a T). Longitudinal: along the length.

  Use it when: Classifying waves.

• Solids shout fastest

  Speed of sound: Solid > Liquid > Gas (SLG).

  Use it when: Comparing media.

• Frequency is loyal to the source

  Change the medium, the frequency stays; speed and wavelength change together.

  Use it when: Media questions.

• Count and multiply by 340

  Seconds between flash and bang × 340 = metres to the storm.

  Use it when: Thunder problems.

Propagation of Sound Waves: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 9-mark question split into 2 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Propagation of Sound Waves

The slips examiners see most often, and what to write instead.

• ✗Mistake: Saying sound is a transverse wave

  Sound in air is longitudinal: particles vibrate along the direction of travel.

  ✓Do this: Link sound with compressions and rarefactions.

  Usually costs: 1 mark.

• ✗Mistake: Changing the frequency when the medium changes

  The frequency is set by the source and stays the same; speed and wavelength change.

  Wrong working

  In water $f=\frac{1500}{{\lambda }_{air}}$

  Right working

  $f$ same; ${\lambda }_{water}=\frac{1500}{f}$

  ✓Do this: Keep $f$ fixed and recalculate $\lambda$.

  Usually costs: 1 to 2 marks.

• ✗Mistake: Thinking amplitude or frequency changes speed

  In a given medium at a given temperature, speed is fixed.

  ✓Do this: Only the medium, temperature and humidity change the speed.

  Usually costs: 1 mark.

• ✗Mistake: Including the light travel time in thunder problems

  It is about a millionth of the sound time and only complicates the answer.

  ✓Do this: State that the time for light is negligible.

  Usually costs: Time; sometimes accuracy.

• ✗Mistake: Taking compression-to-rarefaction distance as λ

  That distance is λ/2.

  ✓Do this: λ is compression to compression.

  Usually costs: The answer.

Practice questions on Propagation of Sound Waves

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   The speed of sound is greatest in:
   (a) air
   (b) water
   (c) steel
   (d) vacuum

   Hint

   Solids fastest.

   Answer

   (c)

2. Q2 · 1 mark · MCQExam level

   In a longitudinal wave, the particles of the medium vibrate:
   (a) perpendicular to the direction of the wave
   (b) along the direction of the wave
   (c) in circles
   (d) not at all

   Hint

   Compressions.

   Answer

   (b)

3. Q3 · 1 mark · Short answerExam level

   A wave has frequency 50 Hz and wavelength 6.6 m. Find its speed.

   Hint

   V = fλ.

   Answer

   330 m s⁻¹.

4. Q4 · 1 mark · Assertion-reasonHarder exam level

   Assertion (A): Astronauts on the Moon cannot hear each other speak directly.
   Reason (R): There is no air on the Moon to carry sound.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Sound needs a medium.

   Answer

   (c)

5. Q5 · 2 marks · Short answerExam level

   A person hears thunder 6 s after seeing lightning. If the speed of sound is 330 m s⁻¹, how far away is the storm?

   Hint

   d = Vt.

   Answer

   1980 m (about 2 km).

6. Q6 · 2 marks · Short answerHarder exam level

   The distance between two consecutive compressions of a sound wave in air is 0.68 m and the speed is 340 m s⁻¹. Find the frequency and the time period.

   Hint

   λ = 0.68 m.

   Answer

   $f=500$ Hz; $T=0.002$ s.

7. Q7 · 3 marks · Short answerHarder exam level

   Sound of wavelength 0.5 m in air (330 m s⁻¹) enters water (1500 m s⁻¹). Find its frequency and its wavelength in water.

   Hint

   f from air data.

   Answer

   $f=660$ Hz; ${\lambda }_w=\frac{1500}{660}\approx 2.27$ m.

8. Q8 · 2 marks · Short answerHarder exam level

   Is the speed of sound in air greater on a hot, humid day or on a cold, dry day? Give a reason for the effect of each factor.

   Hint

   Temperature and humidity.

   Answer

   On the hot, humid day. The speed of sound in air increases as the temperature rises, and it also increases with humidity, because moist air is less dense than dry air.

9. Q9 · 4 marks · Long answerHOTS / competency

   A stone is dropped into a well 45 m deep. The splash is heard 3.13 s after the stone is released. Taking $g=10$ m s⁻², find the speed of sound in the air of the well.

   Hint

   Fall time from S = ½gt².

   Answer

   Fall time: $45=5t^2$, $t=3$ s. Sound time $=0.13$ s. Speed $=\frac{45}{0.13}\approx 346$ m s⁻¹.

10. Q10 · 3 marks · Short answerHarder exam level

    Describe, with a labelled diagram, how a vibrating tuning fork produces compressions and rarefactions in air.

    Hint

    Prong moving out and back.

    Answer

    When a prong moves outward it pushes the air layer next to it, crowding particles into a compression. When it moves back, the air layer spreads out, forming a rarefaction. Repeated vibrations send alternate compressions and rarefactions outward; λ is the distance between two consecutive compressions.

11. Q11 · 2 marks · Short answerHarder exam level

    Two waves in the same medium have frequencies 200 Hz and 400 Hz. Compare their speeds and wavelengths.

    Hint

    Speed depends on the medium.

    Answer

    Same speed; the 400 Hz wave has half the wavelength of the 200 Hz wave.

12. Q12 · 3 marks · Short answerHOTS / competency

    At a 100 m race, the timekeeper at the finish starts the watch on hearing the starting gun instead of seeing the smoke. If sound travels at 340 m s⁻¹, by how much is the recorded time wrong, and is it too long or too short?

    Hint

    Sound takes 100/340 s to arrive.

    Answer

    The watch starts $\frac{100}{340}\approx 0.29$ s late, so the recorded time is about 0.29 s too short.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.What type of wave is sound in air?Show answer

   Longitudinal mechanical wave.

2. 2.Can sound travel through a vacuum?Show answer

   No.

3. 3.In which medium is sound fastest: steel, water or air?Show answer

   Steel.

4. 4.Write the relation between V, f and λ.Show answer

   V = fλ.

5. 5.SI unit of frequency?Show answer

   Hertz (Hz).

6. 6.Approximate speed of sound in air?Show answer

   About 340 m s⁻¹ (330–340 depending on temperature).

7. 7.Why is lightning seen before thunder is heard?Show answer

   Light travels much faster than sound.

8. 8.Does pressure affect the speed of sound at constant temperature?Show answer

   No.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you compare transverse and longitudinal waves?
• ☐Can you describe the bell-jar experiment?
• ☐Can you derive V = fλ from V = λ/T?
• ☐Do you keep f fixed when the medium changes?
• ☐Can you order solids, liquids and gases by speed of sound?
• ☐Can you state the effects of temperature, humidity and pressure?
• ☐Can you find the distance of a storm from the time gap?

Propagation of Sound Waves: frequently asked questions