Wavelength Examples in Physics

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

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

Concept Recap

Wavelength is the distance between two consecutive identical points on a wave, such as from one peak to the next peak or one trough to the next trough.

How 'long' one complete wave cycle is — the spatial size of a single repeating pattern.

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

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

340 \text{ m/s}

and a frequency of

170 \text{ Hz}

. What is the wavelength?

v = 340 m/s, f = 170 Hz → λ = ?

Answer

\lambda = 2 \text{ m}

First step

Use the wave equation:

v = f\lambda

Full solution

2
Rearrange for wavelength: $\lambda = \frac{v}{f}$ .
3
$\lambda = \frac{340}{170} = 2 \text{ m}$

Wavelength is the distance between consecutive identical points on a wave (e.g., crest to crest). It is inversely proportional to frequency for a given wave speed.

Example 2

medium

Red light has a wavelength of

700 \text{ nm}

in a vacuum. What is its frequency? Use

c = 3 \times 10^8 \text{ m/s}

Example 3

medium

A sound wave has frequency 440 Hz and travels at 343 m/s. Find the wavelength.

Example 4

medium

A sound wave in air (

v = 340 \text{ m/s}

) has frequency

1700 \text{ Hz}

. Find its wavelength.

Example 5

medium

A radio station broadcasts at

300 \text{ kHz}

. Find the wavelength. Use

c = 3\times 10^8 \text{ m/s}

Example 6

medium

A tuning fork emits a

256 \text{ Hz}

tone in air (

v = 340 \text{ m/s}

). Find its wavelength.

Example 7

medium

Three wave crests pass a fixed point in

6 \text{ s}

. The wave travels at

4 \text{ m/s}

. Find the wavelength.

Example 8

medium

An ultrasound machine sends

5\text{ MHz}

waves into tissue where they travel at

1540 \text{ m/s}

. Find the wavelength.

Example 9

challenge

A wave on a stretched rope is sketched: between two adjacent peaks the horizontal distance is

0.8 \text{ m}

. The peaks pass a fixed observer at a rate of

5

per second. Find (a) wavelength, (b) frequency, (c) wave speed.

Adjacent peaks 0.8 m apart → λ = 0.8 m, f = 5 Hz, v = 4 m/s

Practice Problems

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

Example 1

easy

A water wave has a wavelength of

3 \text{ m}

and a period of

1.5 \text{ s}

. What is the wave speed?

Example 2

medium

A radio station broadcasts at

98.5 \text{ MHz}

. What is the wavelength of the signal? Use

c = 3 \times 10^8 \text{ m/s}

Example 3

easy

A wave has speed 20 m/s and frequency 5 Hz. Find its wavelength.

v = 20 m/s, f = 5 Hz → find λ

Example 4

easy

On a wave diagram, between which two points do you measure one wavelength?

Peak-to-peak distance = one wavelength

Example 5

easy

A wave has speed 340 m/s and frequency 170 Hz. Find the wavelength.

Example 6

easy

Is wavelength measured horizontally (along travel) or vertically (height) on a transverse wave?

Amplitude is vertical height; wavelength is horizontal distance

Example 7

easy

A wave repeats every 0.25 m. What is its wavelength?

The wave repeats every 0.25 m — what is λ?

Example 8

easy

Convert a wavelength of 200 cm into meters.

Example 9

easy

Wave A has wavelength 2 m and wave B has wavelength 8 m in the same medium and speed. Which has the higher frequency?

Wave A (short λ) vs Wave B (long λ) — which has higher frequency?

Example 10

easy

A wave diagram shows 3 complete cycles spanning 12 m. What is one wavelength?

Example 11

medium

A radio wave travels at 3.0 times 10 to the 8 m/s with frequency 1.0 times 10 to the 8 Hz. Find the wavelength.

Example 12

medium

A sound wave of frequency 256 Hz travels at 343 m/s in air. Find its wavelength (round to two decimals).

Example 13

medium

A wave has wavelength 50 cm and frequency 4 Hz. Find the wave speed in m/s.

Example 14

medium

In the same medium, a wave's frequency triples. By what factor does its wavelength change?

Example 15

medium

A wave's wavelength is 6 m and it passes a point at 2 cycles per second. How far does the wave travel in 5 s?

Example 16

medium

Two consecutive troughs of a water wave are 3 m apart, and the wave passes a buoy 6 times per second. Find the wave speed.

Example 17

medium

A wave graph plots displacement versus position. Two adjacent peaks sit at x = 1 m and x = 5 m. State the wavelength.

Adjacent peaks at x = 1 m and x = 5 m; λ = 5 − 1 = 4 m

Example 18

medium

Why must you convert wavelength to meters before computing wave speed in m/s from frequency in Hz?

Example 19

medium

A wave travels at 24 m/s with frequency 8 Hz. Find its wavelength.

Example 20

challenge

A wave of frequency 100 Hz has wavelength 3.0 m in medium 1. Entering medium 2, its speed increases by 50% while frequency stays the same. Find the new wavelength.

Example 21

challenge

A standing wave on a 1.2 m string fixed at both ends shows 3 antinodes (third harmonic). Find the wavelength.

3rd harmonic: 3 antinodes on 1.2 m string → λ = 0.8 m

Example 22

challenge

A wave's wavelength is reduced from 5 m to 2 m while the medium (and thus speed) is unchanged at 40 m/s. Find the change in frequency.

Example 23

easy

A wave travels at

30 \text{ m/s}

with frequency

15 \text{ Hz}

. Find its wavelength.

v = 30 m/s, f = 15 Hz → λ = ?

Example 24

easy

A wave has speed

12 \text{ m/s}

and frequency

4 \text{ Hz}

. Find its wavelength.

v = 12 m/s, f = 4 Hz → λ = ?

Example 25

medium

Green light has wavelength

500 \text{ nm}

in vacuum. Find its frequency. Use

c = 3\times 10^8 \text{ m/s}

Example 26

easy

A wave has period

0.5 \text{ s}

and speed

8 \text{ m/s}

. Find its wavelength.

T = 0.5 s, v = 8 m/s → λ = vT = 4 m

Example 27

medium

A water wave has wavelength

1.5 \text{ m}

and frequency

2 \text{ Hz}

. How far does the wave travel in

5 \text{ s}

Example 28

easy

A guitar string vibrates so 4 full wavelengths fit in

1.2 \text{ m}

. What is the wavelength?

Example 29

medium

A wave has speed

20 \text{ m/s}

and period

0.4 \text{ s}

. Find the wavelength.

T = 0.4 s, v = 20 m/s → λ = vT = 8 m

Example 30

medium

Microwaves in a microwave oven have frequency

2.45 \text{ GHz}

. Find the wavelength. Use

c = 3\times 10^8 \text{ m/s}

Example 31

easy

A wave repeats every

0.6 \text{ m}

. Find its wavelength.

Wave repeats every 0.6 m → λ = ?

Example 32

hard

A wave traveling at

400 \text{ m/s}

passes from a region where its wavelength is

2 \text{ m}

into a region where the speed is

200 \text{ m/s}

. Find the new wavelength (frequency is unchanged).

Speed halves, frequency unchanged → λ halves from 2 m to 1 m

Example 33

medium

Convert a wavelength of

450 \text{ nm}

(blue light) into meters in scientific notation.

Example 34

easy

A wave with speed

6 \text{ m/s}

has frequency

3 \text{ Hz}

. Find its wavelength.

Example 35

medium

A wave with speed

1500 \text{ m/s}

in water has frequency

600 \text{ Hz}

. Find its wavelength.

Example 36

hard

A standing wave on a

1.0 \text{ m}

string fixed at both ends has 3 antinodes between the ends. What is the wavelength?

3 antinodes on 1.0 m string (3rd harmonic) → λ = 2/3 m ≈ 0.667 m

← Back to Wavelength Formula Explained Common Mistakes Practice Mode

Related Concepts

Waves Frequency Wave Speed

Background Knowledge

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

waves