Wave Speed Examples in Physics

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

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

Concept Recap

Wave speed is the distance a wave pattern travels each second through a medium.

How fast the wave's shape moves forward through whatever it's traveling in.

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: Wave Speed asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to wave speed 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

easy
A sound wave has a frequency of 440 Hz440 \text{ Hz} and a wavelength of 0.773 m0.773 \text{ m}. What is the speed of sound?

Answer

v≈340 m/sv \approx 340 \text{ m/s}

First step

1
Use the wave equation: v=fλv = f\lambda.

Full solution

  1. 2
    Substitute the given values: v=440×0.773v = 440 \times 0.773.
  2. 3
    v=340.1 m/sv = 340.1 \text{ m/s}
The wave equation v=fλv = f\lambda applies to all types of waves. The speed of sound in air at room temperature is approximately 340 m/s340 \text{ m/s}.

Example 2

medium
A seismic wave travels 60 km60 \text{ km} in 10 s10 \text{ s}. What is its speed? If the frequency is 2 Hz2 \text{ Hz}, what is the wavelength?

Example 3

medium
A sound wave has frequency 440 Hz and wavelength 0.773 m. Calculate the speed of sound.

Example 4

medium
A radio wave with wavelength 3 m3 \text{ m} travels at c=3×108 m/sc = 3\times 10^8 \text{ m/s}. Find its frequency.

Example 5

medium
Sound travels at 343 m/s343 \text{ m/s} in air. A whistle at 1715 Hz1715 \text{ Hz} produces sound of what wavelength?

Example 6

hard
A wave on a string has speed v=T/μv = \sqrt{T/\mu}. Find the speed when tension T=250 NT = 250 \text{ N} and linear mass density μ=0.01 kg/m\mu = 0.01 \text{ kg/m}.

Example 7

medium
Sound travels at 343 m/s343 \text{ m/s} in air and 1482 m/s1482 \text{ m/s} in fresh water. By what factor is the wavelength larger in water than in air for the same source frequency?

Example 8

medium
A wave travels 200 m200 \text{ m} in 0.4 s0.4 \text{ s}. If it has frequency 100 Hz100 \text{ Hz}, find its wavelength.

Example 9

hard
A string is replaced by one with four times the linear density, same tension. By what factor does the wave speed change?

Example 10

challenge
A pulse on a rope of mass 0.4 kg0.4 \text{ kg} and length 5 m5 \text{ m} travels at 20 m/s20 \text{ m/s} under some tension. Find the tension.

Practice Problems

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

Example 1

medium
An electromagnetic wave has a frequency of 5×1014 Hz5 \times 10^{14} \text{ Hz}. What is its wavelength? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Example 2

medium
The speed of sound in air at 20°C20°\text{C} is 343 m/s343 \text{ m/s} and in water is 1480 m/s1480 \text{ m/s}. A 500 Hz500 \text{ Hz} tone travels from air into water. Does the frequency or wavelength change? Calculate the wavelength in each medium.

Example 3

easy
A wave has frequency 6 Hz and wavelength 2 m. Find its speed.

Example 4

easy
A wave pattern travels 50 m in 5 s. Find its speed.

Example 5

easy
Sound travels in air at about what speed (to the nearest whole number)?

Example 6

easy
In a given medium, does changing frequency change the wave speed?

Example 7

easy
A wave has wavelength 0.5 m and frequency 100 Hz. Find its speed.

Example 8

easy
Wave speed is the speed of the pattern or the speed of the medium's particles?

Example 9

easy
In which medium is sound generally fastest: gas, liquid, or solid?

Example 10

easy
A wave travels 24 m in 3 s. Find its speed.

Example 11

medium
A wave with frequency 8 Hz has wavelength 250 cm. Find its speed in m/s.

Example 12

medium
Sound travels at 343 m/s in air. How long does thunder take to reach you from 1715 m away?

Example 13

medium
A wave's period is 0.5 s and its wavelength is 6 m. Find its speed.

Example 14

medium
Light travels at 3.0 times 10 to the 8 m/s. How far does it travel in 2 s (give in meters)?

Example 15

medium
A wave moves at 30 m/s with frequency 15 Hz. Find its wavelength.

Example 16

medium
A wave's speed in medium 1 is 200 m/s. In medium 2 it slows to 150 m/s while frequency stays at 50 Hz. Find the wavelength in medium 2.

Example 17

medium
You see lightning and hear thunder 6 s later. Using sound speed 343 m/s (light effectively instant), how far away was the strike?

Example 18

medium
A wave has period 0.02 s and wavelength 0.5 m. Find its speed.

Example 19

medium
A wave covers 45 m in 9 s. Find its speed, and if its frequency is 2.5 Hz, its wavelength.

Example 20

challenge
A wave travels 360 m in 1.5 minutes and you count 270 complete cycles passing a point during that time. Find the speed, frequency, and wavelength.

Example 21

challenge
An echo returns 0.4 s after a shout off a cliff. Using sound speed 343 m/s, how far away is the cliff?

Example 22

challenge
A wave's speed doubles when entering a new medium while its frequency is unchanged. A student claims the wavelength stays the same. Show the student is wrong and find the new wavelength factor.

Example 23

easy
A wave has frequency 20 Hz20 \text{ Hz} and wavelength 0.5 m0.5 \text{ m}. Find its speed.

Example 24

easy
A wave travels 120 m120 \text{ m} in 4 s4 \text{ s}. Find its speed.

Example 25

medium
A wave on a rope has speed 24 m/s24 \text{ m/s} and period 0.3 s0.3 \text{ s}. Find its wavelength.

Example 26

medium
A wave's frequency triples while its wavelength halves. By what factor does the wave speed change?

Example 27

easy
A wave has wavelength 4 m4 \text{ m} and frequency 7 Hz7 \text{ Hz}. Find its speed.

Example 28

medium
An earthquake P-wave reaches a station 800 km800 \text{ km} away in 100 s100 \text{ s}. Find its speed.

Example 29

medium
A light pulse takes 1.28 s1.28 \text{ s} to travel from the Moon to Earth. Estimate the Earth–Moon distance.

Example 30

easy
A wave has period 0.2 s0.2 \text{ s} and wavelength 5 m5 \text{ m}. Find its speed.

Example 31

hard
A guitar string is 0.65 m0.65 \text{ m} long, has linear density μ=5×10−3 kg/m\mu = 5\times 10^{-3} \text{ kg/m}, and is tuned so the fundamental frequency is 110 Hz110 \text{ Hz}. Find the wave speed on the string.

Example 32

easy
A wave has frequency 50 Hz50 \text{ Hz} and wavelength 0.04 m0.04 \text{ m}. Find its speed.

Example 33

medium
An ocean wave has wavelength 40 m40 \text{ m} and period 8 s8 \text{ s}. Find its speed.

Example 34

medium
Light in glass has refractive index n=1.5n = 1.5. Find its speed in glass.

Example 35

easy
A wave has speed 15 m/s15 \text{ m/s} and wavelength 3 m3 \text{ m}. Find its frequency.
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Background Knowledge

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

wavelengthfrequency