Speed of Sound Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Speed of Sound.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The speed of sound is how fast a sound wave travels through a medium.

Sound moves faster in some materials than in others because the medium's particles pass the disturbance along differently.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Speed of Sound asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to speed of sound but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Wave Speed Mistakes

Worked Examples

Example 1

medium

You see lightning and hear thunder

7.5\text{ s}

later. Using

340\text{ m/s}

, how far away is the strike?

Answer

d = 2550 m

First step

Light arrives almost instantly; sound delay equals travel time.

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Example 2

medium

A 440 Hz tuning fork has wavelength

0.78\text{ m}

outdoors. Estimate the air temperature using

v \approx 331 + 0.6 T_C

(in

\text{m/s}

T_C

^\circ\text{C}

Example 3

hard

Use

v = 331 + 0.6 T_C

(m/s) to find the speed of sound at

T_C = -10^\circ\text{C}

and at

T_C = 30^\circ\text{C}

, and the percent change.

Example 4

hard

A stone is dropped into a well. Splash heard

2.0\text{ s}

later. Using

g = 9.8\text{ m/s}^2

and ignoring the sound delay, find the well depth; then check if the sound delay (at

340\text{ m/s}

) matters at the percent level.

Example 5

challenge

If the air temperature rises from

273\text{ K}

373\text{ K}

, by what factor does the speed of sound change? (Use

v\propto\sqrt{T}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A sound wave has frequency 200 Hz and wavelength 1.5 m. Find its speed.

Example 2

easy

Sound travels at 340 m/s. A wave has frequency 170 Hz. Find its wavelength.

Example 3

easy

A wave of wavelength 0.5 m moves at 343 m/s in air. Find its frequency.

Example 4

easy

Does sound travel faster in air or in steel?

Example 5

easy

Sound travels 686 m in 2 seconds in air. What is its speed?

Example 6

easy

A wave moves at 343 m/s with period 0.01 s. Find its wavelength. (

\lambda = v T

Example 7

easy

True or false: the wave speed equals the speed of the air molecules oscillating.

Example 8

easy

A 500 Hz sound has wavelength 0.68 m. Find the speed of sound in this medium.

Example 9

medium

You see lightning and hear thunder 5 seconds later. Using 340 m/s for sound, how far away is the strike?

Example 10

medium

A boat sends sonar straight down; the echo returns in 0.4 s. If sound travels 1500 m/s in water, how deep is the seabed?

Example 11

medium

Sound of frequency 256 Hz has wavelength 1.34 m in air. What is its wavelength in water, where sound travels 1500 m/s, at the same frequency?

Example 12

medium

On a hot day sound travels at 350 m/s; on a cold day at 330 m/s. A 700 Hz tone is played on both days. Find the wavelength difference.

Example 13

medium

A wave travels 1020 m in 3 s. Find its frequency if the wavelength is 1.7 m.

Example 14

medium

Two observers stand 680 m apart. A starter pistol fires near observer A. How long after observer A hears it does observer B hear it? (Use 340 m/s.)

Example 15

medium

An echo off a cliff returns in 1.5 s. Using 340 m/s, how far away is the cliff?

Example 16

medium

A tuning fork at 440 Hz produces sound with wavelength 0.773 m on a warm day. Estimate the speed of sound that day.

Example 17

medium

A wave has frequency 425 Hz and travels at 340 m/s. Find its wavelength.

Example 18

challenge

A whistle of frequency 1000 Hz is on a cliff edge. Sound travels at 340 m/s and the wavelength is asked at two temperatures: 340 m/s and 360 m/s. Find the percentage increase in wavelength.

Example 19

challenge

A car horn blasts at 500 Hz. The car moves toward a wall and the driver hears an echo. Ignoring Doppler, if the wall is 170 m away and sound is 340 m/s, how long until the driver first hears the echo (car stationary)?

Example 20

challenge

Sound speed in a gas is

v=\sqrt{\frac{\gamma R T}{M}}

. If absolute temperature

T

increases from 288 K to 320 K, by what factor does the speed increase?

Example 21

easy

A wave has frequency

250\text{ Hz}

and wavelength

1.36\text{ m}

. Find its speed.

Example 22

easy

Sound travels at

343\text{ m/s}

and has wavelength

0.5\text{ m}

. Find its frequency.

Example 23

easy

400\text{ Hz}

tone has wavelength

0.85\text{ m}

in air. Find the sound speed.

Example 24

easy

Sound covers

850\text{ m}

2.5\text{ s}

. Find its speed.

Example 25

easy

A wave has period

T = 2.0\times10^{-3}\text{ s}

in air at

v = 340\text{ m/s}

. Find its wavelength.

Example 26

easy

1000\text{ Hz}

tone travels at

340\text{ m/s}

. Find its wavelength.

Example 27

medium

Sonar echo from a submarine returns in

0.8\text{ s}

v = 1500\text{ m/s}

in water. Find the distance.

Example 28

medium

A 256 Hz tuning fork is held over water. Its wavelength in water is

5.86\text{ m}

. Find the speed of sound in water.

Example 29

medium

An echo from a wall returns in

0.6\text{ s}

when sound speed is

343\text{ m/s}

. Find the wall's distance.

Example 30

medium

A 200 Hz wave has wavelength

1.65\text{ m}

on a cool day. Find the speed.

Example 31

medium

Two friends stand 510 m apart. One shouts; how long until the other hears at

340\text{ m/s}

Example 32

medium

Sound in steel travels at

5000\text{ m/s}

. A

1\text{ kHz}

wave: find the wavelength.

Example 33

medium

A clap echoes off a cliff

171\text{ m}

away. Using

342\text{ m/s}

, find the echo time.

Example 34

medium

A 2.0 kHz wave in air (

v = 340\text{ m/s}

) crosses into water (

v_w = 1500\text{ m/s}

). Frequency stays the same. Find the new wavelength.

Example 35

medium

An ultrasound at

5\text{ MHz}

travels in tissue at

1540\text{ m/s}

. Find the wavelength.

Example 36

hard

An observer hears a starter pistol

0.5\text{ s}

after seeing the smoke; visible-light delay is negligible. If air is

343\text{ m/s}

, how far away is the pistol?

Example 37

hard

Two pulses are sent along a

200\text{ m}

steel rail. One travels through steel (

v_s = 5000\text{ m/s}

), one through air (

v_a = 340\text{ m/s}

). Find the time gap between them at the far end.

Example 38

hard

A wave with

\lambda = 0.5\text{ m}

travels at

340\text{ m/s}

. How many cycles fit in a

4.25\text{ m}

tube?

Example 39

hard

Bats use

50\text{ kHz}

chirps. In air (

v = 340\text{ m/s}

), find the wavelength.

Example 40

hard

A sonar pulse in seawater (

v = 1530\text{ m/s}

) takes

1.6\text{ s}

round-trip. Find the depth to the seafloor.

Example 41

challenge

Using

v = \sqrt{\gamma R T/M}

with

\gamma = 1.4

R = 8.314\text{ J/(mol K)}

M = 0.029\text{ kg/mol}

, compute the speed of sound at

T = 300\text{ K}

Example 42

challenge

A train horn at

400\text{ Hz}

has wavelength

0.85\text{ m}

in still air. The train moves at

30\text{ m/s}

toward a stationary listener. Find the wavelength of the sound between train and listener in front (use

\lambda' = \lambda - v_s/f

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Related Concepts

Sound Wave Speed

Background Knowledge

These ideas may be useful before you work through the harder examples.

soundwave speed