Period Examples: 44 Problems with Answers

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

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

Concept Recap

The time required for one complete cycle of a repeating wave or oscillation to occur, measured in seconds.

How long it takes a swing to go all the way and come back to where it started.

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

Common stuck point: Students often know a formula related to period 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

medium

A sound wave has frequency

f = 440\text{ Hz}

(A above middle C). Find its period in milliseconds.

Answer

T \approx 2.27 ms

First step

T = 1/f = 1/440 \approx 2.27\times10^{-3}\text{ s}

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Example 2

medium

A spring oscillates with

40

cycles in

5\text{ s}

. Find its period and frequency.

Example 3

hard

An EM wave in vacuum has wavelength

\lambda = 600\text{ nm}

(visible green). Find its period (

c = 3\times10^8\text{ m/s}

Example 4

hard

A wave's period changes from

T_1 = 0.5\text{ s}

T_2 = 0.1\text{ s}

. By what factor does its frequency change?

Example 5

challenge

Two tuning forks have periods

T_1 = 2.50\text{ ms}

and

T_2 = 2.55\text{ ms}

. Find the beat frequency you would hear.

Practice Problems

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

Example 1

easy

A wave has frequency

f = 4

Hz. Find its period.

Example 2

easy

A pendulum completes one swing back-and-forth in

2

s. What is its period?

Example 3

easy

A wave has period

T = 0.5

s. Find its frequency.

Example 4

easy

What are the units of period?

Example 5

easy

A heart beats

60

times per minute. What is the period of one beat?

Example 6

easy

A wave repeats every

0.1

s. What is its frequency?

Example 7

easy

Does a higher-frequency wave have a longer or shorter period?

Example 8

easy

A wave makes

20

complete cycles in

5

s. Find its period.

Example 9

medium

A wave has frequency

f = 250

Hz. Find its period in milliseconds.

Example 10

medium

A pulse repeats with period

T = 2

ms. Find its frequency in Hz.

Example 11

medium

A wave travels at

v = 20

m/s with wavelength

\lambda = 4

m. Find its period.

Example 12

medium

A wave has period

T = 0.25

s and travels at

v = 8

m/s. Find its wavelength.

Example 13

medium

An EM wave in vacuum has period

T = 1\times10^{-8}

s. Find its frequency.

Example 14

medium

A wave completes

1500

cycles in

30

s. Find its period.

Example 15

medium

Two waves: wave X has

T = 0.01

s, wave Y has

f = 50

Hz. Which has the higher frequency?

Example 16

medium

A swing has period

T = 3

s. How many complete cycles does it make in

1

minute?

Example 17

medium

A wave has frequency

f = 125

Hz. Find its period in milliseconds.

Example 18

challenge

A wave's frequency increases from

f

4f

. By what factor does its period change?

Example 19

challenge

A wave travels

30

m in

6

s and has wavelength

\lambda = 2

m. Find its period.

Example 20

challenge

An EM wave in vacuum has wavelength

\lambda = 6

m. Find its period (use

c = 3\times10^8

m/s).

Example 21

easy

A wave has frequency

f = 5\text{ Hz}

. Find its period.

Example 22

easy

A pendulum completes

30

swings in

60\text{ s}

. Find its period.

Example 23

easy

A wave has period

T = 0.4\text{ s}

. Find its frequency.

Example 24

easy

A buoy bobs up and down completing one cycle every

3\text{ s}

. What is its period?

Example 25

easy

A signal repeats every

250\text{ ms}

. Find its frequency in Hz.

Example 26

medium

A wave has period

T = 8\text{ ms}

. Find its frequency in Hz.

Example 27

medium

A wave travels at

v = 12\text{ m/s}

with wavelength

\lambda = 3\text{ m}

. Find its period.

Example 28

medium

A wave has period

T = 0.5\text{ s}

and travels at

v = 6\text{ m/s}

. Find its wavelength.

Example 29

medium

An FM radio station broadcasts at

100\text{ MHz}

. Find its period.

Example 30

medium

A metronome ticks at

120\text{ BPM}

(beats per minute). Find its period in seconds.

Example 31

medium

A wave has frequency

f = 200\text{ Hz}

in a medium where its wavelength is

\lambda = 1.5\text{ m}

. Find its period and wave speed.

Example 32

medium

A simple pendulum of length

L = 1.0\text{ m}

has period

T = 2\pi\sqrt{L/g}

(

g = 9.8

). Find

T

Example 33

medium

A laser oscillates at frequency

5\times10^{14}\text{ Hz}

. Find its period in femtoseconds (

1\text{ fs} = 10^{-15}\text{ s}

Example 34

medium

A wave's frequency drops from

400\text{ Hz}

250\text{ Hz}

. By what factor does its period change?

Example 35

hard

A wave on a string has

\lambda = 0.6\text{ m}

and travels at

v = 24\text{ m/s}

. Find its period in milliseconds.

Example 36

hard

A mass-on-spring oscillator has

T = 2\pi\sqrt{m/k}

. For

m = 0.25\text{ kg}

and

k = 100\text{ N/m}

, find

T

Example 37

hard

Two pendulums on Earth:

L_1 = 1.0\text{ m}

L_2 = 4.0\text{ m}

. Find the ratio

T_2/T_1

Example 38

hard

A wave travels

48\text{ m}

4\text{ s}

and has wavelength

\lambda = 4\text{ m}

. Find its period.

Example 39

challenge

A pendulum on the Moon has the same length as one on Earth. If

g_\text{Moon} = 1.6\text{ m/s}^2

and

g_\text{Earth} = 9.8\text{ m/s}^2

, find

T_\text{Moon}/T_\text{Earth}

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Related Concepts

Frequency Waves Wave Speed Simple Harmonic Motion

Background Knowledge

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

frequencywaves