PhysicsICSE Class 9 · Propagation of Sound Waves

Wave Motion, Longitudinal Sound Waves and the Wave Equation V = fλ (ICSE Class 9)

Updated 17 October 2026 · Fact-checked

A wave carries energy without carrying the medium. In a transverse wave particles vibrate at right angles to the direction of travel (crests and troughs); in a longitudinal wave, such as sound in air, they vibrate along it (compressions and rarefactions). Wave speed V = fλ = λ/T. When sound enters a new medium, f stays the same while V and λ change.

Understand Wave Motion, Longitudinal Sound Waves and V = fλ

Wave motion. A wave is a disturbance that carries energy from one place to another; in a mechanical wave the particles of the medium only vibrate about their mean positions and pass the disturbance on.

	Transverse wave	Longitudinal wave
Particle vibration	Perpendicular to the direction of travel	Along the direction of travel
Shape	Crests and troughs	Compressions and rarefactions
Examples	Waves on a string, ripples on water	Sound in air, pulse on a slinky
Media	Needs a medium that resists change of shape (solids, liquid surfaces)	Solids, liquids and gases

Sound. A vibrating body (tuning fork, vocal cords, drum skin) pushes the air layer next to it forward to form a compression (high pressure) and then pulls back to leave a rarefaction (low pressure). These travel outward, so sound in air is a longitudinal mechanical wave and needs a medium; it cannot travel through a vacuum (bell-jar experiment: the bell is seen striking but is not heard when the air is pumped out).

Terms.

Amplitude: maximum displacement from the mean position.
**Time period $T$ : time for one complete vibration; frequency $f$ :** vibrations per second (hertz), $f = \frac{1}{T}$ .
**Wavelength $λ$ :** distance between two consecutive compressions (or rarefactions, crests, troughs); the distance the wave travels in one time period.
**Wave speed $V$ :** distance travelled per second.

Wave equation. In one period the wave moves one wavelength:

$V = \frac{λ}{T} = f λ .$

So at a fixed speed a higher frequency means a shorter wavelength.

Change of medium. The source fixes the frequency. When sound enters another medium the frequency is unchanged, the speed changes, and so the wavelength changes: $λ = \frac{V}{f}$ . For a faster medium the wavelength is longer.

Counting. Number of compressions passing a point per second $= f$ . From one compression to the next rarefaction is $\frac{λ}{2}$ .

Graphs. A displacement–distance graph shows wavelength (crest to crest); a displacement–time graph shows time period.

Sound or light? Light is not a mechanical wave and travels through a vacuum; sound needs a medium.

Wave Motion, Longitudinal Sound Waves and V = fλ: formulas and key facts

Wave equation: $V = f λ = \frac{λ}{T}$; V in m s⁻¹, λ in m, f in Hz.
Frequency and period: $f = \frac{1}{T}$; Hz = s⁻¹.
Change of medium: $f_{1} = f_{2}; \frac{λ _{1}}{λ _{2}} = \frac{V _{1}}{V _{2}}$; Frequency constant.

How to solve Wave Motion, Longitudinal Sound Waves and V = fλ questions

Identify which two of V, f, λ, T are given.

1Convert wavelength to metres and frequency to hertz (1 kHz = 1000 Hz).
2Use $V = f λ$ for the missing quantity; use $T = 1/ f$ for the period.
3Across a boundary keep $f$ fixed and find the new wavelength from the new speed.
4For counting problems use "number per second = f".
5Quote the SI unit with each answer.

Wave Motion, Longitudinal Sound Waves and V = fλ in real life

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.

A flute in a hall

Suppose a flute plays a note of frequency 850 Hz in a hall where the speed of sound is 340 m s⁻¹.

Find the wavelength and the time period.

Try it first, then show the solutionSolution

$λ = \frac{V}{f} = \frac{340}{850} = 0.4$ m.
$T = \frac{1}{850} \approx 1.18 \times 1 0^{- 3}$ s.

Answer: 0.4 m and about 1.18 ms.

Memory hook: λ = V ÷ f.

Tricks to remember Wave Motion, Longitudinal Sound Waves and V = fλ

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

Along or across
Longitudinal: along (like pushing a slinky). Transverse: across (like shaking a rope).
Use it when: Types of wave.
Source sets f
Frequency belongs to the source; speed belongs to the medium.
Use it when: Change-of-medium problems.
V = fλ triangle
Cover the unknown in a triangle with V on top and f, λ below.
Use it when: Rearranging.

Wave Motion, Longitudinal Sound Waves and V = fλ: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Compression · 1 mark · MCQBoard level

In a sound wave travelling in air, a compression is a region where the air is:
(a) at lower pressure and more spread out
(b) at higher pressure and more crowded
(c) at rest
(d) moving only upward

Try it first, then show the solutionSolution

Compressions have particles crowded together, giving higher pressure.

Answer: (b)

Example 2: Tuning fork · 2 marks · Short answerBoard level

A tuning fork of frequency 320 Hz produces sound in air with speed 340 m s⁻¹. Find the wavelength and the time period.

Try it first, then show the solutionSolution

$λ = \frac{V}{f} = \frac{340}{320} \approx 1.06$ m. (1)
$T = \frac{1}{f} = \frac{1}{320} \approx 3.1 \times 1 0^{- 3}$ s. (1)

Answer: 1.06 m; 3.1 ms

Example 3: Waves on a rope · 3 marks · Short answerHarder board level

12 crests of a wave on a rope pass a fixed point in 6 s. The distance between consecutive crests is 0.25 m. Find the frequency, the speed of the wave, and the distance a crest moves in 10 s.

Try it first, then show the solutionSolution

$f = \frac{12}{6} = 2$ Hz. (1)
$V = f λ = 2 \times 0.25 = 0.5$ m s⁻¹. (1)
Distance $= 0.5 \times 10 = 5$ m. (1)

Answer: 2 Hz; 0.5 m s⁻¹; 5 m

Example 4: Entering a new medium · 3 marks · Short answerHarder board level

A note of frequency 600 Hz travels in air at 340 m s⁻¹ and then enters another medium where its wavelength is 2.5 m. Find the wavelength in air, the speed in the new medium, and the factor by which the wavelength has increased.

Try it first, then show the solutionSolution

$λ_{ai r} = \frac{340}{600} \approx 0.567$ m. (1)
The frequency stays 600 Hz: $V = 600 \times 2.5 = 1500$ m s⁻¹. (1)
Factor $= \frac{2.5}{0.567} \approx 4.4$ (equal to $\frac{1500}{340}$ ). (1)

Answer: 0.567 m; 1500 m s⁻¹; about 4.4 times

Example 5: A loudspeaker · 4 marks · Case-basedHOTS / competency

A loudspeaker sends a 425 Hz sound into air where the distance between consecutive compressions is 0.8 m.
(a) Find the speed of sound and the time period.
(b) How many compressions pass a microphone each second?
(c) What is the distance from the centre of a compression to the centre of the next rarefaction?
(d) On a warmer day the speed becomes 346 m s⁻¹ for the same speaker. Find the new wavelength.

Try it first, then show the solutionSolution

(a) $V = 425 \times 0.8 = 340$ m s⁻¹; $T = \frac{1}{425} \approx 2.35$ ms. (1)
(b) 425 per second. (1)
(c) $\frac{λ}{2} = 0.4$ m. (1)
(d) $f$ stays 425 Hz: $λ = \frac{346}{425} \approx 0.814$ m. (1)

Answer: (a) 340 m s⁻¹; 2.35 ms (b) 425 (c) 0.4 m (d) 0.814 m

Where students lose marks in Wave Motion, Longitudinal Sound Waves and V = fλ

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

Mistake: Wavelength in cm used with speed in m s⁻¹
Units must agree.
Wrong working
V = 500 × 68 = 34 000
Right working
V = 500 × 0.68 = 340 m s⁻¹
Do this: Convert to metres first.
Usually costs: The answer.
Mistake: Frequency said to change in a new medium
It is fixed by the source.
Wrong working
f becomes 4.4 times as large.
Right working
f is unchanged; λ and V change.
Do this: Say "source sets f".
Usually costs: The reasoning mark.
Mistake: Sound called a transverse wave
Air cannot support transverse waves; sound is longitudinal.
Wrong working
Sound is transverse with crests and troughs.
Right working
Sound is longitudinal with compressions and rarefactions.
Do this: Learn the two examples.
Usually costs: 1 mark.

Exam tips

Write V = fλ, then substitute with units.
State "frequency is unchanged" in every change-of-medium answer.
Name compressions and rarefactions when describing sound.
Give the bell-jar result as evidence that sound needs a medium.

Practice questions on Wave Motion, Longitudinal Sound Waves and V = fλ

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

Q1 · 1 mark · MCQBoard level
In a transverse wave the particles of the medium vibrate:
(a) along the direction of the wave
(b) at right angles to the direction of the wave
(c) not at all
(d) in circles only
Hint
Definition.
Answer
(b)
Q2 · 1 mark · Very short answerBoard level
State the SI unit of frequency.
Hint
Named after a physicist.
Answer
Hertz (Hz).
Q3 · 2 marks · Short answerHarder board level
Find the wavelength in air of a sound of frequency 1.7 kHz (speed 340 m s⁻¹).
Hint
Convert to Hz.
Answer
$λ = \frac{340}{1700} = 0.2$ m.
Q4 · 3 marks · Short answerHarder board level
The time period of a wave is 4 ms and its wavelength is 1.32 m. Find its frequency and speed.
Hint
Convert ms to s.
Answer
$f = \frac{1}{0.004} = 250$ Hz; $V = 250 \times 1.32 = 330$ m s⁻¹.
Q5 · 2 marks · Assertion-reasonHarder board level
Assertion (A): The frequency of a sound does not change when it passes from air into water.
Reason (R): The frequency is determined by the source of the sound.
(a) Both true, R explains A.
(b) Both true, R does not explain A.
(c) A true, R false.
(d) A false, R true.
Hint
Source vs medium.
Answer
(a)
Q6 · 3 marks · Short answerHOTS / competency
A graph of a sound wave in air (speed 330 m s⁻¹) shows three complete wavelengths over a distance of 4.5 m. Find the wavelength, the frequency and the time period.
Hint
Three wavelengths in 4.5 m.
Answer
$λ = \frac{4.5}{3} = 1.5$ m; $f = \frac{330}{1.5} = 220$ Hz; $T = \frac{1}{220} \approx 4.5$ ms.

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.Wave equation?Show answer
V = fλ.
2.Type of wave for sound in air?Show answer
Longitudinal, mechanical.
3.Wavelength in a longitudinal wave?Show answer
Distance between two consecutive compressions.
4.What changes when sound enters a new medium?Show answer
Speed and wavelength (not frequency).
5.Does sound travel in vacuum?Show answer
No.

Wave Motion, Longitudinal Sound Waves and V = fλ: frequently asked questions

What is the relation V = fλ?

Wave speed equals frequency times wavelength, because a wave travels one wavelength in one time period.

Why is sound a longitudinal wave?

The particles of air vibrate along the direction in which the wave moves, producing compressions and rarefactions.

Does the wavelength change when sound enters water from air?

Yes, it becomes longer because the speed is greater while the frequency stays the same.