Frequency Examples in Physics: 88 Problems with Answers

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

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 number of complete wave cycles passing a fixed point per second, measured in hertz (Hz).

How many times something vibrates per second—high frequency means very rapid vibration.

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

Common stuck point: Students often know a formula related to frequency 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 pendulum completes

20

swings in

40 \text{ s}

. What is its frequency and period?

Answer

f = 0.5 Hz, T = 2 s

First step

Use the definition of frequency: cycles per second.

Full solution

2
Frequency: $f = \frac{number of cycles}{time} = \frac{20}{40} = 0.5 Hz$
3
Period: $T = \frac{1}{f} = \frac{1}{0.5} = 2 s$

Frequency is the number of complete oscillations per second, measured in hertz (Hz). Period is the time for one complete oscillation and is the reciprocal of frequency.

Example 2

medium

A radio station broadcasts at

100 \text{ MHz}

. What is the wavelength of the radio wave? Use

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

Example 3

easy

A guitar string vibrates at

G_4 = 196 \text{ Hz}

. How long does one full vibration take?

Example 4

medium

A pendulum of length

L = 1 \text{ m}

swings on Earth where

g = 9.8 \text{ m/s}^2

. Find its frequency.

Example 5

medium

FM radio broadcasts in the band

88

–

108 \text{ MHz}

. What is the wavelength range of FM radio signals? Use

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

Example 6

medium

A car horn emits

f = 440 \text{ Hz}

. The car approaches a stationary listener at

v_{\text{car}} = 20 \text{ m/s}

. Sound speed is

343 \text{ m/s}

. What frequency does the listener hear?

Example 7

hard

Two tuning forks of frequencies

440 \text{ Hz}

and

444 \text{ Hz}

are sounded together. What is the beat frequency heard?

Example 8

hard

A car moves toward you at

30 \text{ m/s}

. Its horn frequency is

500 \text{ Hz}

. After it passes, what frequency do you hear? Use

v_{\text{sound}} = 343 \text{ m/s}

Example 9

hard

A photon has energy

E = 3.0 \text{ eV}

. Find its frequency. Use

h = 6.63 \times 10^{-34} \text{ J}\cdot \text{s}

and

1 \text{ eV} = 1.602\times 10^{-19} \text{ J}

Example 10

hard

An RLC circuit with

L = 10 \text{ mH}

C = 100 \text{ nF}

. What is the resonant frequency in kHz?

Example 11

hard

An EM wave has a wavelength of

1 \text{ Å}

(

10^{-10} \text{ m}

). What is its frequency? Use

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

Example 12

challenge

Two trains approach each other, each at

30 \text{ m/s}

. One sounds a horn at

500 \text{ Hz}

. What frequency does the listener on the other train hear? Use

v_{\text{sound}} = 343 \text{ m/s}

Example 13

medium

A sound wave travels in air at

343\text{ m/s}

with wavelength

0.5\text{ m}

. Find its frequency.

Example 14

medium

A piano key vibrates at

262\text{ Hz}

(middle C). How many full cycles occur in

5\text{ s}

Example 15

hard

Two pianos play notes at

440\text{ Hz}

and

444\text{ Hz}

simultaneously. What is the beat frequency?

Example 16

medium

A water wave travels at

3 \text{ m/s}

with wavelength

0.6 \text{ m}

. Find its frequency.

Example 17

hard

A wave travels

480 \text{ m}

4 \text{ s}

and has wavelength

60 \text{ cm}

. Find its frequency.

Practice Problems

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

Example 1

easy

A wave has a period of

0.02 \text{ s}

. What is its frequency?

Example 2

medium

A guitar string vibrates at a fundamental frequency of

330 \text{ Hz}

. What are the frequencies of the second and third harmonics? If the string length is

easy

A wave completes

300

cycles in

1

minute. What is its frequency in Hz?

Example 24

easy

AC household voltage in North America oscillates at

60 \text{ Hz}

. How many full cycles occur in

1 \text{ s}

Example 25

medium

A sound wave travels at

v = 343 \text{ m/s}

in air with wavelength

0.686 \text{ m}

. What is its frequency?

Example 26

medium

A mass-spring system has

k = 250 \text{ N/m}

and

m = 0.4 \text{ kg}

. What is its oscillation frequency?

Example 27

medium

Visible green light has wavelength

\lambda = 550 \text{ nm}

. Find its frequency. Use

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

Example 28

medium

A standing wave forms on a guitar string of length

L = 0.65 \text{ m}

. The wave speed on the string is

v = 286 \text{ m/s}

. What is the fundamental frequency?

Example 29

medium

A bat emits ultrasonic chirps at

f = 50 \text{ kHz}

. What is the wavelength in air at

v = 343 \text{ m/s}

Example 30

hard

An organ pipe closed at one end has length

L = 0.50 \text{ m}

. What are the first two resonant frequencies? Use

v = 343 \text{ m/s}

Example 31

hard

An LC circuit has

L = 5 \text{ mH}

and

C = 20 \text{ μF}

. What is its resonant frequency?

Example 32

hard

A wheel rotates at

1200 \text{ rpm}

. What is its rotational frequency in Hz, and its angular speed

\omega

in rad/s?

Example 33

hard

A simple pendulum on the Moon (

g_M = 1.62 \text{ m/s}^2

) has

L = 1 \text{ m}

. How does its frequency compare with the same pendulum on Earth (

g_E = 9.81 \text{ m/s}^2

Example 34

easy

A pendulum makes

30

complete swings in

60\text{ s}

. Find its frequency.

Example 35

easy

A wave has a period of

0.05\text{ s}

. What is its frequency?

Example 36

easy

A heart beats

72

times per minute. What is the heartbeat frequency in Hz?

Example 37

easy

A wave on a string has period

T = 0.25\text{ s}

. Find its frequency.

Example 38

medium

A light wave in vacuum has frequency

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

. Find its wavelength in nm. Use

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

Example 39

medium

A guitar string is plucked and vibrates at

440\text{ Hz}

. Find its period in milliseconds.

Example 40

medium

An FM radio station broadcasts at

98\text{ MHz}

. Find the wavelength of its signal. Use

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

Example 41

medium

A wave travels at

20\text{ m/s}

with wavelength

0.4\text{ m}

. Find its frequency.

Example 42

medium

A sonar pulse has frequency

25\text{ kHz}

in water where sound travels at

1500\text{ m/s}

. Find its wavelength.

Example 43

medium

A clock's quartz crystal oscillates at

32{,}768\text{ Hz}

. How long is one oscillation, in microseconds?

Example 44

hard

A string of length

0.5\text{ m}

fixed at both ends has wave speed

200\text{ m/s}

. Find the fundamental frequency.

Example 45

hard

A radar emits microwaves at

10\text{ GHz}

. Find the wavelength in cm. Use

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

Example 46

hard

An ambulance siren at

700\text{ Hz}

approaches a stationary observer at

30\text{ m/s}

. Find the observed frequency (Doppler). Use

v_{\text{sound}} = 340\text{ m/s}

Example 47

medium

A wave makes

300

complete cycles in

1

minute. Find its frequency in Hz and its period.

Example 48

medium

A wave of frequency

5\text{ Hz}

travels at

10\text{ m/s}

. Find its wavelength.

Example 49

challenge

A photon of light has frequency

f

. Its energy is

E = hf

where

h = 6.626\times 10^{-34}\text{ J s}

. Find the energy of a photon with

and frequency

170 \text{ Hz}

. Find its wavelength.

Example 56

medium

A radio wave has frequency

500 \text{ kHz}

. Find its wavelength. Use

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

Example 57

medium

A wave passes 240 wave crests in 1 minute. Find its frequency in Hz.

Example 58

medium

Light has speed

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

and a green wavelength of

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

. Find its frequency.

Example 59

medium

Two tuning forks vibrate at

440 \text{ Hz}

and

441 \text{ Hz}

. They are heard together. What is the beat frequency?

Example 60

medium

A wave has wavelength

2.5 \text{ m}

and frequency

120 \text{ Hz}

. Find its speed.

Example 61

medium

A wave of frequency

50 \text{ Hz}

and wavelength

4 \text{ m}

enters a new medium where its speed doubles. What is its new wavelength?

Example 62

medium

An oscillator runs at

60 \text{ MHz}

. Find the period in nanoseconds.

Example 63

hard

A guitar string fixed at both ends has length

0.5 \text{ m}

and wave speed

400 \text{ m/s}

. Find the fundamental frequency.

Example 64

hard

An open-ended pipe of length

0.85 \text{ m}

has speed of sound

340 \text{ m/s}

. Find its fundamental frequency.

Example 65

hard

A microwave oven operates at

2.45 \text{ GHz}

. Find the wavelength. Use

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

Example 66

hard

A simple pendulum of length

1 \text{ m}

swings with period

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

. Find its frequency. Use

g = 9.8 \text{ m/s}^2

Example 67

hard

A stationary observer hears a

500 \text{ Hz}

siren on an ambulance approaching at

34 \text{ m/s}

. With sound speed

340 \text{ m/s}

, what frequency does the observer hear?

Example 68

hard

A guitar string has fundamental frequency

200 \text{ Hz}

. What are the frequencies of its 2nd, 3rd, and 4th harmonics?

Example 69

hard

An electric guitar string's fundamental is

330 \text{ Hz}

. To raise the pitch by an octave (double the frequency), by what factor must the wave speed change if length is constant?

Example 70

challenge

Two waves of frequencies

498 \text{ Hz}

and

502 \text{ Hz}

are superimposed. How many beats per second are heard, and what is the average tone frequency?

Example 71

challenge

A wave on a string has frequency

25 \text{ Hz}

, wavelength

0.4 \text{ m}

, and travels along a

4 \text{ m}

string. How long does the wave take to travel the full string length?

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Related Concepts

Waves Wavelength Period

Background Knowledge

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

waves