Intensity Examples: 46 Problems with Answers

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

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

Concept Recap

Wave intensity is the power carried by a wave through each unit of area.

Intensity tells you how concentrated the wave's energy flow is.

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

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

Intensity at

2\,\text{m}

from a point source is

12\,\text{W/m}^2

. Find intensity at

8\,\text{m}

Answer

I = 0.75 {W/m}^{2}

First step

Ratio of distances

8/2 = 4

, so ratio of

r^2

16

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Example 2

medium

A point source has intensity

100\,\text{W/m}^2

1\,\text{m}

. Find intensity at

5\,\text{m}

Example 3

hard

A search-light radiates

2000\,\text{W}

uniformly into a cone covering

1/20

of the full sphere. Find the intensity at

50\,\text{m}

Practice Problems

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

Example 1

easy

A speaker emits 12 W of sound power spread evenly over an area of 4 m^2. What is the intensity?

Example 2

easy

A wave delivers 50 W through a window of area 2 m^2. Find the intensity.

Example 3

easy

Intensity of a wave is 8 W/m^2 over an area of 5 m^2. What total power passes through?

Example 4

easy

Which quantity does intensity describe: total energy, power per unit area, or frequency?

Example 5

easy

A lamp radiates 100 W uniformly over a sphere of area 50 m^2. Find the intensity at that surface.

Example 6

easy

If intensity is 6 W/m^2 and the area is 3 m^2, what is the power?

Example 7

easy

Two surfaces receive the same power but one has twice the area. Which has lower intensity?

Example 8

easy

A wave carries 24 W through an area of 8 m^2. What is the intensity?

Example 9

medium

A point source emits 200 W. What is the intensity at a distance of 5 m? (Sphere area

A=4\pi r^2

Example 10

medium

The intensity 2 m from a point source is 9 W/m^2. What is the intensity at 6 m?

Example 11

medium

A source gives intensity 16 W/m^2 at 3 m. At what distance is the intensity 4 W/m^2?

Example 12

medium

A 60 W source spreads power over a hemisphere of radius 2 m (

A=2\pi r^2

). Find the intensity.

Example 13

medium

If you double the power of a point source and keep distance fixed, how does intensity change?

Example 14

medium

A wave's intensity is 12 W/m^2 over a circular detector of radius 1 m (

A=\pi r^2

). How much power does it collect?

Example 15

medium

At 4 m a source gives 2 W/m^2. What total power does the source emit? (

A=4\pi r^2

Example 16

medium

Source A and B emit equal power. You stand 3 m from A and 6 m from B. Which sounds more intense and by what factor?

Example 17

medium

A point source produces intensity 32 W/m^2 at 1 m. Find the intensity at 4 m.

Example 18

challenge

Two point sources each emit 80 W. They sit 10 m apart. Find the total intensity at the midpoint. (

A=4\pi r^2

Example 19

challenge

A point source's intensity at distance

r

I_0

. By what factor must you increase

r

to reduce intensity to

I_0/100

Example 20

challenge

A source radiates 100 W into a cone covering 1/10 of a full sphere. Find the intensity at 3 m. (Full sphere area

4\pi r^2

Example 21

easy

A loudspeaker outputs

20\,\text{W}

of sound power spread evenly over an area of

10\,\text{m}^2

. Find the intensity.

Example 22

easy

A wave's intensity is

5\,\text{W/m}^2

at a window of area

4\,\text{m}^2

. How much power passes through?

Example 23

easy

A wave delivers

90\,\text{W}

across an area of

30\,\text{m}^2

. Find the intensity.

Example 24

easy

An ultrasound source emits

0.5\,\text{W}

uniformly through a probe face of area

5 \times 10^{-4}\,\text{m}^2

. Find the intensity.

Example 25

easy

A wall of area

8\,\text{m}^2

receives sound intensity

0.5\,\text{W/m}^2

. How much total acoustic power hits the wall?

Example 26

easy

A 40 W point source radiates into a full sphere of radius

1\,\text{m}

(

A = 4\pi r^2

). Find the intensity at

1\,\text{m}

Example 27

medium

A point source has intensity

I_0

at distance

r

. Find the intensity at distance

2r

Example 28

medium

A point source emits

500\,\text{W}

. Find the intensity at

10\,\text{m}

(

A = 4\pi r^2

Example 29

medium

Intensity at

5\,\text{m}

from a point source is

4\,\text{W/m}^2

. At what distance is the intensity

1\,\text{W/m}^2

Example 30

medium

A laser beam carries

2\,\text{W}

in a uniform circular spot of radius

1\,\text{mm}

. Find the intensity in

\text{W/m}^2

Example 31

medium

A point source's intensity drops from

36\,\text{W/m}^2

r

4\,\text{W/m}^2

. By what factor did the distance grow?

Example 32

medium

3\,\text{m}

from a point source the intensity is

8\,\text{W/m}^2

. Find the source's total power (

A = 4\pi r^2

Example 33

medium

A hemisphere lamp of total power

80\,\text{W}

radiates into a hemisphere (

A = 2\pi r^2

). Find intensity at

4\,\text{m}

Example 34

medium

The Sun delivers about

1361\,\text{W/m}^2

at the top of Earth's atmosphere. A solar panel of area

2\,\text{m}^2

faces the Sun above the atmosphere. What incoming power does it intercept?

Example 35

hard

A point source has intensity

9\,\text{W/m}^2

4\,\text{m}

. At what distance is the intensity

1\,\text{W/m}^2

Example 36

hard

Two identical point sources each emit

50\,\text{W}

. Source A is

2\,\text{m}

away; source B is

4\,\text{m}

away. Find the total intensity (assume incoherent addition,

A = 4\pi r^2

Example 37

hard

A point source has intensity

I_0

r

. A point at distance

5r

then receives intensity ____ in terms of

I_0

Example 38

hard

A speaker radiates

25\,\text{W}

uniformly into a forward hemisphere (

A = 2\pi r^2

). Find the intensity at

5\,\text{m}

on-axis.

Example 39

hard

A point source's intensity at

r

I_0

. If the source's power is doubled and the listener moves to

2r

, find the new intensity.

Example 40

hard

For a wave on a stretched string, intensity is proportional to amplitude squared. If amplitude triples (same frequency, medium), how does intensity change?

Example 41

challenge

Two identical isotropic sources, each

40\,\text{W}

, sit

8\,\text{m}

apart. Find the total (incoherent) intensity at the midpoint (

A = 4\pi r^2

Example 42

challenge

A point source's intensity is

I_0

r

. By what factor must

r

grow to reduce the intensity to

I_0/64

Example 43

challenge

A solar panel of area

1.5\,\text{m}^2

converts

20\%

of incident sunlight to electricity. With solar intensity

1000\,\text{W/m}^2

at its surface, find the electrical power output.

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Related Concepts

Amplitude Loudness

Background Knowledge

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

amplitude