Practice Amplitude in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The maximum displacement of a wave from its equilibrium (rest) position, measuring the wave's strength or intensity.

How 'tall' the wave is measured from the center line — bigger amplitude carries more energy and produces stronger effects.

Showing a random 20 of 76 problems.

Example 1

easy

A pendulum swings

8 \text{ cm}

to the right and

8 \text{ cm}

to the left of its rest position. What is its amplitude?

Example 2

medium

A sound's amplitude is halved. By what factor does its energy (proportional to amplitude squared) change?

When amplitude is halved, by what factor does the wave energy change?

Example 3

challenge

A wave's energy is 100 J at amplitude A. To raise its energy to 225 J in the same medium, what amplitude (as a multiple of A) is needed (energy proportional to amplitude squared)?

Example 4

hard

A seismic wave's amplitude drops to

1/3

of its initial value after travelling a certain distance. What fraction of its initial energy remains?

Example 5

medium

A wave on a string has amplitude

0.1 \text{ m}

and frequency

2 \text{ Hz}

. The string has a linear mass density of

0.05 \text{ kg/m}

and the wave speed is

10 \text{ m/s}

. What is the power transmitted by the wave? Use

P = \frac{1}{2}\mu\omega^2 A^2 v

Example 6

medium

Two coherent waves with amplitudes

A_1 = 3 \text{ cm}

and

A_2 = 4 \text{ cm}

overlap in phase. What is the resulting amplitude?

Constructive interference: waves of amplitude 3 cm and 4 cm add in phase to give 7 cm.

Example 7

challenge

A damped oscillator's amplitude decays as

A(t) = A_0 e^{-\gamma t}

. If the amplitude falls to half its initial value in

4 \text{ s}

, find

\gamma

, and predict the amplitude (as a fraction of

A_0

) after

12 \text{ s}

Example 8

easy

A water wave's surface rises

0.25 \text{ m}

above calm level at its crest. What is the amplitude of the wave?

Example 9

hard

A spherical wave radiates from a point source isotropically. At

r_1 = 2 \text{ m}

its amplitude is

A_1 = 0.1

. Ignoring absorption, what is the amplitude at

r_2 = 10 \text{ m}

Example 10

medium

A wave's amplitude is 5 cm. After traveling through a damping medium, its amplitude drops to 1 cm. What fraction of its original energy remains (energy proportional to amplitude squared)?

Amplitude drops from 5 cm to 1 cm after passing through the damping medium. What fraction of energy remains?

Example 11

medium

A simple pendulum of length

1 \text{ m}

has amplitude

0.05 \text{ m}

(small angle). What is its maximum angular displacement from vertical, in radians?

Example 12

medium

A wave's amplitude doubles. By what factor does its energy (proportional to amplitude squared) increase?

When amplitude doubles, by what factor does the wave energy increase?

Example 13

medium

A radio carrier wave has amplitude

200 \text{ mV}

at the antenna and

20 \text{ mV}

at the receiver. By what factor has the wave amplitude decreased? By what factor has the carried power decreased?

Example 14

hard

A string carries a transverse wave with

\mu = 0.02 \text{ kg/m}

v = 8 \text{ m/s}

, frequency

f = 5 \text{ Hz}

, and amplitude

A = 0.04 \text{ m}

. Compute the time-averaged power transmitted,

P = \tfrac{1}{2}\mu \omega^2 A^2 v

Example 15

medium

A wave on a string is described by

y(x,t) = 0.05 \sin(2x - 6t) \text{ m}

. Identify the amplitude, wave number, and angular frequency.

Example 16

challenge

Two speakers play the same note in phase, each producing amplitude 3 units at a point. Find the combined amplitude and how the combined energy compares to one speaker alone (energy proportional to amplitude squared).

Example 17

easy

Wave A has amplitude 2 cm and wave B has amplitude 6 cm (same wave type). Which carries more energy?

Wave A has amplitude 2 cm; wave B has amplitude 6 cm. Which carries more energy?

Example 18

medium

Wave

A

has amplitude

2 \text{ cm}

and wave

B

has amplitude

6 \text{ cm}

(same medium, same frequency). How does the energy carried by wave

B

compare to that carried by wave

A

Wave A has amplitude 2 cm; wave B has amplitude 6 cm (same medium, same frequency). Compare their energies.

Example 19

easy

An oscilloscope shows a sinusoidal voltage signal with peak-to-peak value

12 \text{ V}

. What is the amplitude of the signal?

Oscilloscope trace with peak-to-peak value 12 V. What is the amplitude?

Example 20

medium

A microphone records a sound wave with displacement amplitude

5 \times 10^{-8} \text{ m}

. If the loudness is increased so the new displacement amplitude is

5 \times 10^{-7} \text{ m}

, by what factor has the intensity changed?

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Related Concepts

Waves Intensity Energy