CDS Physics · Sound

Waves and the Speed of Sound

Longitudinal and transverse waves, why sound needs a medium, the wave equation v = f × λ, and how fast sound travels in solids, liquids and gases.

All Sound notes

Why this matters

Ten CDS questions from 2018 (I) to 2026 (I). Three ask about the two kinds of wave and why sound needs a medium, three are one-line sums on the wave equation, and four compare the speed of sound in different media or with the speed of light.

Concept 1 of 3: Longitudinal and transverse waves

A wave carries energy from place to place while the particles of the medium only shake about their own positions. If they shake back and forth along the direction the wave travels, the wave is longitudinal: think of pushing and pulling a slinky along its length. If they shake at right angles to that direction, the wave is transverse: think of flicking a rope up and down. Sound in air is longitudinal. Light is transverse, and it needs no material to travel through.

Definition

Two kinds of wave:

Longitudinal: particles move along the direction of the wave. The wave is a train of compressions and rarefactions, which are changes in density. Sound in air is longitudinal, and longitudinal waves can travel in solids, liquids and gases.
Transverse: particles move perpendicular to the direction of the wave, as crests and troughs. These need the medium to resist a change of shape, so mechanical transverse waves travel through solids (and along a liquid surface) but not through a gas.
Light is an electromagnetic wave: its electric and magnetic fields vibrate across the direction of travel, so it is transverse, and it needs no medium.
Sound is a mechanical wave: it needs a material medium and cannot travel through a vacuum.
Superposition: where two waves meet, the displacement of each particle is the algebraic sum of the two displacements.

Wave	Type and medium
Sound in air	Longitudinal: compressions and rarefactions; needs a mediumQ CDS 2023 (I): sound and light in air are longitudinal and transverse respectively.
Light	Transverse electromagnetic wave; travels through a vacuum
Wave along a stretched string	Transverse; needs the string
Ripples on water	Transverse at the surface
Sound in a vacuum	Cannot travel: there is no mediumQ CDS 2018 (I): sound cannot pass through a hollow pipe kept in a vacuum.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2026 · CDS (I) 2026 — General Knowledge · Q20Moderate

Example 1 · Sound · Waves and the Speed of Sound

Consider the following statements regarding waves : 1. If the particles of a medium move along the direction of motion of the wave, the wave is called a longitudinal wave. 2. If the particles of a medium move perpendicular to the direction of motion of the wave, the wave is called a transverse wave. 3. Transverse waves may involve change in the shape of the medium, whereas longitudinal waves involve change in the density of the medium. Which of the statements given above is/are correct ?

Sound and light are opposite kinds of wave

In air, sound is longitudinal and light is transverse. An option calling them both longitudinal, both transverse, or swapping the order is the usual trap.

A solid inside a vacuum still carries sound; a vacuum does not

Sound travels through any solid, liquid or gas, including a copper wire or a glass prism. What stops it is empty space: the inside of a pipe in a vacuum has no medium at all.

Drill 2 more on longitudinal and transverse waves

Concept 2 of 3: The wave equation: speed, frequency and wavelength

In one time period, a wave moves forward by exactly one wavelength. The frequency is how many waves pass each second. So in one second the wave moves forward by frequency × wavelength, and that is its speed. Every wave sum in CDS is this one line, sometimes with distance = speed × time added on.

Definition

The words and the one equation:

Frequency $f$ : complete waves (oscillations) per second, in hertz (Hz). One crest plus one trough is one complete wave.
Time period $T$ : time for one complete wave, $T = 1/f$ .
Wavelength $\lambda$ : length of one complete wave, crest to crest.
Speed: $v = f\lambda$ . The time to cover a distance $d$ is $d/v$ .
N wavelengths take N periods, so the time is $N/f$ whatever the wavelength.

Wave equation

v = f\,\lambda \qquad T = \frac{1}{f} \qquad t = \frac{d}{v}

vspeed of the wave, in m/s
ffrequency, in Hz
$\lambda$ wavelength, in m
Ttime period, in s
t, dtime taken and distance covered

Worked example

A sound wave has a frequency of 500 Hz and a wavelength of 68 cm. Find its speed, and the time it takes to travel 1.7 km.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (II) 2021 — General Knowledge · Q19Moderate

Example 2 · Sound · Waves and the Speed of Sound

A sound wave has a frequency of 4 kHz and wavelength 30 cm. How long will it take to travel 2·4 km ?

A crest and a trough together make one wave

Twenty crests with twenty troughs are twenty complete waves, not forty. Count pairs, then divide by the time to get the frequency.

Convert to metres and seconds first

A wavelength in centimetres or a distance in kilometres must be changed to metres before using

v = f\lambda

, and kilohertz to hertz. Most wrong options come from a missed factor of 100 or 1000.

Drill 2 more on the wave equation: speed, frequency and wavelength

Concept 3 of 3: Speed of sound in different media

Sound passes from particle to particle, so it goes fastest where the particles are held most tightly together and spring back hardest. That is why it is fastest in solids, slower in liquids and slowest in gases. Light is far faster still: about a million times faster than sound in air, which is why you see lightning before you hear its thunder.

Definition

What sets the speed of sound:

Solids > liquids > gases. A stiffer medium carries sound faster: steel (about 5960 m/s) beats glass (about 3980 m/s for flint glass).
In water, dissolved salt makes the medium stiffer: sea water (about 1531 m/s) is faster than distilled water (about 1498 m/s).
In air, the speed rises with temperature: about 331 m/s at 0 °C and 346 m/s at 25 °C.
Light in air travels at about $3 \times 10^{8}$ m/s, so a flash arrives almost at once and the sound arrives later: thunder and lightning.
Supersonic: faster than sound. A source moving faster than sound leaves a cone-shaped shock wave, heard as a sonic boom.

Medium	Speed of sound (m/s, NCERT values)
Aluminium	6420
Steel	5960Q CDS 2023 (II): of glass, stainless steel, water and oxygen, sound is fastest in steel.
Glass (flint)	3980
Sea water	1531Q CDS 2024 (II): sea water is faster than distilled water, drinking water or methanol.
Distilled water	1498
Methanol	1103
Air at 25 °C	346
Oxygen	316

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2023 · CDS (II) 2023 — General Knowledge · Q35Moderate

Example 3 · Sound · Waves and the Speed of Sound

In which of the following media is the speed of sound the maximum ?

Denser is not the rule; stiffer is

Sound is fastest in solids because they are stiff (hard to compress), not simply because they are heavy. That is why steel beats glass and sea water beats fresh water. Among gases, the lighter hydrogen carries sound faster than oxygen.

A sonic boom needs a speed above the speed of sound, not light

A sonic boom comes from a source moving faster than sound. Nothing with mass can move faster than light, so that option is always wrong; moving exactly at or below the speed of sound gives no boom.

Drill 3 more on speed of sound in different media

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

The wave equation: speed, frequency and wavelength
Wave equation
$v = f\,\lambda \qquad T = \frac{1}{f} \qquad t = \frac{d}{v}$

Reference tables (2)

Longitudinal and transverse waves5 rows

Wave	Type and medium
Sound in air	Longitudinal: compressions and rarefactions; needs a mediumQ CDS 2023 (I): sound and light in air are longitudinal and transverse respectively.
Light	Transverse electromagnetic wave; travels through a vacuum
Wave along a stretched string	Transverse; needs the string
Ripples on water	Transverse at the surface
Sound in a vacuum	Cannot travel: there is no mediumQ CDS 2018 (I): sound cannot pass through a hollow pipe kept in a vacuum.

Speed of sound in different media8 rows

Medium	Speed of sound (m/s, NCERT values)
Aluminium	6420
Steel	5960Q CDS 2023 (II): of glass, stainless steel, water and oxygen, sound is fastest in steel.
Glass (flint)	3980
Sea water	1531Q CDS 2024 (II): sea water is faster than distilled water, drinking water or methanol.
Distilled water	1498
Methanol	1103
Air at 25 °C	346
Oxygen	316

Watch out for (6)

Sound and light are opposite kinds of wave
→ Longitudinal and transverse waves
A solid inside a vacuum still carries sound; a vacuum does not
→ Longitudinal and transverse waves
A crest and a trough together make one wave
→ The wave equation: speed, frequency and wavelength
Convert to metres and seconds first
→ The wave equation: speed, frequency and wavelength
Denser is not the rule; stiffer is
→ Speed of sound in different media
A sonic boom needs a speed above the speed of sound, not light
→ Speed of sound in different media

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