Waves Examples in Physics

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

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

Concept Recap

A disturbance that transfers energy and information through space or a medium without permanently displacing the matter it travels through.

Energy traveling through something—like ripples on water. The water stays put; the ripple moves.

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

Common stuck point: Students often know a formula related to waves 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 wave has a frequency of 5 Hz5 \text{ Hz} and a wavelength of 2 m2 \text{ m}. What is the wave speed? How far does the wave travel in 10 s10 \text{ s}?

Answer

v=10 m/s,d=100 mv = 10 \text{ m/s}, \quad d = 100 \text{ m}

First step

1
Use the wave equation: v=fλ=5×2=10 m/sv = f\lambda = 5 \times 2 = 10 \text{ m/s}.

Full solution

  1. 2
    Distance traveled in 10 s10 \text{ s}: d=vt=10×10=100 md = vt = 10 \times 10 = 100 \text{ m}
  2. 3
    In 10 s10 \text{ s}, 5050 complete waves pass any fixed point (55 per second for 1010 seconds).
A wave is a disturbance that transfers energy without transferring matter. The wave equation v=fλv = f\lambda relates the three fundamental wave properties: speed, frequency, and wavelength.

Example 2

medium
A wave pulse travels along a rope at 4 m/s4 \text{ m/s}. The rope is 12 m12 \text{ m} long with one end fixed. How long does it take for the pulse to travel to the fixed end and return?

Example 3

medium
A transverse wave on a string has speed 20 m/s20 \text{ m/s} and frequency 50 Hz50 \text{ Hz}. (a) What is its wavelength? (b) How far does a wave crest travel in 0.6 s0.6 \text{ s}?

Example 4

medium
A longitudinal sound wave travels through air at 343 m/s343 \text{ m/s}. A tuning fork creates a wave with wavelength 0.686 m0.686 \text{ m}. What is the period of the wave?

Example 5

medium
A pulse on a stretched spring travels 9 m9 \text{ m} in 1.5 s1.5 \text{ s}. Another pulse with twice the amplitude is sent down the same spring. What is the speed of the second pulse?

Example 6

medium
A tsunami in deep water travels at about 200 m/s200 \text{ m/s}. If its wavelength is 400 km400 \text{ km}, how many minutes pass between successive crests at a fixed point in the ocean?

Example 7

hard
A wave on a string is described by y(x,t)=0.02sin⁡(8x−24t)y(x,t) = 0.02 \sin(8x - 24t) in SI units. Find (a) amplitude, (b) wavelength, (c) frequency, and (d) speed.

Example 8

hard
An observer hears a 1000 Hz1000 \text{ Hz} siren on a stationary ambulance. The ambulance then moves toward the observer at 34 m/s34 \text{ m/s}. If the speed of sound is 340 m/s340 \text{ m/s}, what frequency does the observer hear?

Example 9

hard
A wave on a string has equation y=0.03sin⁡(2π(5x−20t))y = 0.03 \sin(2\pi(5x - 20t)) in SI units. Determine the wave's direction of travel and its speed.

Example 10

hard
Light of wavelength 500 nm500 \text{ nm} in vacuum enters a glass medium with refractive index n=1.5n = 1.5. What is the wavelength inside the glass? (Frequency does not change at a boundary.)

Example 11

challenge
A guitar string of length 0.65 m0.65 \text{ m} has wave speed 260 m/s260 \text{ m/s}. What are the frequencies of the first three harmonics (modes with n=1,2,3n = 1, 2, 3 half-wavelengths)?

Example 12

easy
A wave's amplitude doubles while everything else stays the same. By what factor does the energy carried by the wave change?

Practice Problems

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

Example 1

medium
Water waves in a ripple tank have a wavelength of 0.03 m0.03 \text{ m} and travel at 0.12 m/s0.12 \text{ m/s}. What is the frequency? How many complete waves pass a point in 15 s15 \text{ s}?

Example 2

hard
A wave on a string has the equation y(x,t)=0.05sin⁡(4πx−8πt)y(x,t) = 0.05 \sin(4\pi x - 8\pi t) (SI units). What are the amplitude, wavelength, frequency, and wave speed?

Example 3

easy
A wave moves across a pond. What does the wave transfer from one place to another?

Example 4

easy
True or false: a leaf floating on water is carried across the pond by a passing water wave.

Example 5

easy
Which type of wave can travel through a vacuum: a sound wave or a light wave?

Example 6

easy
A wave is described as a 'disturbance.' What is the equilibrium state it disturbs?

Example 7

easy
Name the two broad categories of waves based on whether they need a medium.

Example 8

easy
A wave passes through a string. Do the string particles travel along the string with the wave?

Example 9

easy
Give one everyday example of a mechanical wave.

Example 10

easy
What is conserved as a wave moves matter back and forth: the matter's position or the matter's energy that gets passed along?

Example 11

medium
A wave on a rope completes 5 full oscillations as it travels. If each oscillation corresponds to one wavelength of 0.4 m, how far has the wave pattern advanced?

Example 12

medium
A mechanical wave and an electromagnetic wave both reach a region of vacuum. Which one continues, and why?

Example 13

medium
Two waves carry energy. Wave A has double the amplitude of Wave B (same frequency, same medium). Qualitatively, which carries more energy?

Example 14

medium
A wave's pattern travels 12 m in 4 s. What is the speed of the pattern?

Example 15

medium
Sound from a bell and light from a flash leave at the same instant from a distant lighthouse. Which reaches you first, and what does that tell you about wave speeds?

Example 16

medium
A buoy bobs up and down 30 times in 60 s as waves pass. How many complete oscillations does it make per second?

Example 17

medium
Explain why two boats far apart can each rock in place even though the same wave passes both.

Example 18

medium
A wave's frequency is doubled in the same medium while speed stays fixed. What happens to its wavelength?

Example 19

medium
Why is space described as 'silent' even when stars explode?

Example 20

challenge
A wave travels 600 m in a medium in 2.0 s. Along the way you count 150 complete wavelengths. Find the wavelength and the frequency.

Example 21

challenge
A wave carries power proportional to (amplitude squared) times frequency squared. Wave A has triple the amplitude and one-third the frequency of Wave B. Compare their power.

Example 22

challenge
A pulse takes 0.50 s to travel down a 10 m rope and reflect back to the start. What is the wave speed on the rope?

Example 23

easy
A sound wave has frequency f=200 Hzf = 200 \text{ Hz} and wavelength λ=1.7 m\lambda = 1.7 \text{ m}. What is the wave speed?

Example 24

easy
A water wave travels at 3 m/s3 \text{ m/s} with wavelength 0.5 m0.5 \text{ m}. What is its frequency?

Example 25

easy
A wave on a string has amplitude A=0.04 mA = 0.04 \text{ m}. What is the maximum displacement of a point on the string from equilibrium?

Example 26

medium
Two waves traveling in the same medium have frequencies f1=100 Hzf_1 = 100 \text{ Hz} and f2=400 Hzf_2 = 400 \text{ Hz}. The wave speed is the same. What is the ratio λ1/λ2\lambda_1/\lambda_2?

Example 27

medium
An ocean wave travels 48 m48 \text{ m} in 12 s12 \text{ s}. If its wavelength is 6 m6 \text{ m}, what is its frequency?

Example 28

medium
A wave is described by y(x,t)=0.05sin⁡(4πx−10πt)y(x,t) = 0.05 \sin(4\pi x - 10\pi t) where xx and yy are in meters and tt is in seconds. What is the wave's speed?

Example 29

medium
Two transverse pulses on a rope move toward each other. Pulse A has amplitude +3 cm+3 \text{ cm}, pulse B has amplitude −2 cm-2 \text{ cm}. At the instant they overlap completely, what is the displacement of the rope?

Example 30

medium
Microwaves in a microwave oven have frequency 2.45 GHz2.45 \text{ GHz}. What is their wavelength in air? Use c=3.0×108 m/sc = 3.0 \times 10^8 \text{ m/s}.

Example 31

hard
A wave on a stretched string has speed v1=30 m/sv_1 = 30 \text{ m/s}. The tension is quadrupled. What is the new wave speed?

Example 32

hard
Two speakers 1 m1 \text{ m} apart emit sound waves in phase at frequency f=680 Hzf = 680 \text{ Hz} (sound speed 340 m/s340 \text{ m/s}). A listener directly in front of one speaker hears constructive or destructive interference? Justify with a path difference calculation.

Example 33

hard
A standing wave on a string fixed at both ends shows 3 antinodes between the ends. The string is 1.5 m1.5 \text{ m} long. What is the wavelength?

Example 34

challenge
A bat emits ultrasonic pulses at 40 kHz40 \text{ kHz} and flies toward a stationary wall at 5 m/s5 \text{ m/s}. The sound speed is 340 m/s340 \text{ m/s}. What frequency does the bat detect for the reflected echo?
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Background Knowledge

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

energysimple harmonic motion