Transverse Wave Examples in Physics

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

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 wave in which the particles of the medium oscillate perpendicular to the direction of wave propagation.

Shake a rope side-to-side: the wave travels along the rope, but the rope moves up and down.

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

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

Worked Examples

Example 1

easy

A transverse wave on a rope has a wavelength of

1.5 \text{ m}

and a frequency of

4 \text{ Hz}

. What is the wave speed? In which direction do the rope particles move relative to the wave's direction?

Answer

v = 6 \text{ m/s}; \text{ particles move perpendicular to wave direction}

First step

Wave speed:

v = f\lambda = 4 \times 1.5 = 6 \text{ m/s}

Full solution

2
In a transverse wave, particles oscillate perpendicular to the wave's direction of travel.
3
If the wave moves horizontally along the rope, the rope particles move up and down (vertically).

In a transverse wave, the oscillation of the medium is perpendicular to the direction of wave propagation. Examples include waves on strings, water surface waves, and electromagnetic waves.

Example 2

medium

A transverse wave on a string has a speed of

20 \text{ m/s}

. The string has a tension of

80 \text{ N}

. What is the linear mass density of the string?

Example 3

medium

A transverse wave on a string has tension

T = 50 \text{ N}

and linear mass density

\mu = 0.02 \text{ kg/m}

. Find the wave speed.

Example 4

medium

A guitar string of length

0.65 \text{ m}

vibrates at its fundamental frequency

440 \text{ Hz}

. Find the wave speed.

Example 5

hard

A string of mass

20 \text{ g}

and length

4 \text{ m}

is under

80 \text{ N}

tension. Find the speed of a transverse pulse.

Example 6

medium

A polarizing filter blocks one transverse polarization of light. Why doesn't this work for sound waves in air?

Example 7

hard

A string with

\mu = 0.01 \text{ kg/m}

carries a transverse wave

y(x,t) = (0.04 \text{ m})\sin(8x - 32t)

, units SI. Find tension

T

Example 8

challenge

Two strings (linear densities

\mu

and

4\mu

) are tied end-to-end at the same tension. A transverse wave going from the lighter to the heavier string has its speed change by what factor?

Example 9

medium

An ocean wave has wavelength

40 \text{ m}

and travels at

8 \text{ m/s}

. What is the period?

Example 10

medium

A transverse wave on a string has

v = 120 \text{ m/s}

. If the tension is quadrupled (mass density unchanged), find the new speed.

Example 11

hard

A standing transverse wave on a fixed-end string of length

1.2 \text{ m}

shows three nodes (including ends). The wave speed is

300 \text{ m/s}

. Find the frequency.

Practice Problems

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

Example 1

medium

Explain why transverse waves can travel through solids but not through fluids (liquids and gases). Give an example of each.

Example 2

hard

A guitar string (

\mu = 0.003 \text{ kg/m}

, length

0.65 \text{ m}

) is tuned to play a note at

easy

A transverse wave on a string has wavelength

2 \text{ m}

and frequency

10 \text{ Hz}

. Find its speed.

Example 24

easy

A transverse pulse takes

0.4 \text{ s}

to travel along a

20 \text{ m}

rope. Find its speed.

Example 25

medium

Light is a transverse electromagnetic wave with speed

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

. A red beam has frequency

4.6 \times 10^{14} \text{ Hz}

. Find its wavelength.

Example 26

medium

A transverse wave has amplitude

5 \text{ cm}

and angular frequency

20 \text{ rad/s}

. Find the maximum transverse particle speed.

Example 27

easy

A transverse wave has period

0.25 \text{ s}

. Find its frequency.

Example 28

medium

Two adjacent crests of a transverse wave on a rope are

0.8 \text{ m}

apart and pass a fixed point at

5 \text{ crests/s}

. Find the wave speed.

Example 29

easy

Doubling a transverse wave's frequency at the same speed does what to its wavelength?

Example 30

medium

A transverse wave travels at

30 \text{ m/s}

along a rope. What frequency yields a

0.5 \text{ m}

wavelength?

Example 31

easy

Transverse waves can travel through solids because solids have ___ that fluids lack.

Example 32

medium

The frequency of a transverse wave on a string under tension is doubled by the source. The wave speed and wavelength change as ___.

Example 33

easy

A rope wave has amplitude

0.10 \text{ m}

. By how much do rope particles displace from equilibrium at maximum?

Example 34

medium

An EM wave in vacuum has wavelength

500 \text{ nm}

. Find its frequency.

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Related Concepts

Waves Longitudinal Wave Polarization

Background Knowledge

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

waves