SOUND LEVELS:

POWER AND

INTENSITYLeslie Liu

Learning Object

Power and Intensity

Power: energy emitted by sound waves over a

given period of time

Units: (J/s or Watts)

Intensity: amount of energy carried by sound

waves per unit time through a given area

Commonly referred to as the “loudness” of a

sound

Units: (Watts/m2)

Sound waves with high intensity have a high

energy and therefore a high amplitude

Power and Intensity

The intensity of a sound decreases the further

you move away from the source

We understand this intuitively, but let’s explain it

with physics!

Intensity is the amount of energy emitted by

sound waves per unit time (power) through a

given area

Power and Intensity

The energy emitted by a sound wave remains

constant over time and doesn’t change with

distance (conservation of energy)

Increasing the distance from the source

(radius) increases the area covered by the

sound wave

Power and Intensity

If the power of the sound wave remains the

same and the area covered by the wave

increases, then the intensity will decrease the

further away we move from the source

Example with Numbers:

I1 = P/A I2 = P/A

I1 = 10W/5m2 I2 = 10W/10m2

I1 = 2 W/m2 I2 = 1 W/m2

Power and Intensity

The intensity of a sound wave is uniformly

distributed at the same distance

Moving around a point at a constant distance will

produce no change in intensity or “loudness”

Note: for 3D waves, the area a sound wave

travels through is a sphere

Therefore

PhET Simulation

This simulation shows how intensity is

uniformly distributed at the same distance

http://phet.colorado.edu/en/simulation/sound

Question 1:

1) Assuming that sound waves fronts are 3D

spherical shells, how do the intensities

compare if located 1.0m (I1) and 4.0m (I4)

away from the sound source?

A) I1/I4 = 16

B) I1/I4 = 1/4

C) I1/I4 = 1/16

D) I1/I4 = 4

E) Not enough information

Question 1: Answer

A) I1/I4 = 16

1) Use the formula for intensity

2) Set the two formulas as a ratio of each other

3) Simplify expression

4) Since the power of the wave is the same,

they cancel out and you are left with

Question 2:

2) A person is standing beside a speaker as it

plays a 10,000 Hz tone. The sound waves

travel away from the speaker uniformly in all

directions. If the distance from the speaker

doubles, then the intensity of the waves that

the person observes:

A) doesn’t change

B) halves

C) decreases by a factor of 4

D) decreases by a factor of 8

Question 2: Answer

C) decreases by a factor of 4

The energy of the sound wave remains the

same but the surface area it covers changes

Recall that

At 1m away, the area covered is 4π

At 2m away, the area covered is 16π

As the distance doubles, the value in the

denominator increases by a factor of 4

Therefore, the intensity decreases by a factor

of 4

Question 2: Answer

The intensity follows a 1/r2 relationship

Question 3:

3) A person is standing beside a speaker as it

plays a 10,000 Hz tone. The sound waves

travel away from the speaker uniformly in all

directions. If the distance from the speaker

doubles, then the amplitude of the waves that

the person observes:

A) doesn’t change

B) halves

C) decreases by a factor of 4

D) decreases by a factor of 8

Question 3: Answer

B) halves

Recall that the energy of a wave is

proportional to the square of its amplitude

Energy of a wave is represented by power (P)

in the equation for intensity

Therefore intensity is also proportional to the

square of the wave’s amplitude

By rearranging this relationship, we find that

the amplitude is proportional to the square root

of intensity

Question 3: Answer

From the previous question we determined

that the intensity decreases by a factor of 4

when the distance doubles

Taking the square root of ¼ gives us ½

Therefore, the amplitude halves when the

distance doubles

Sound, Interference, and Pressure PhET

Simulation http://phet.colorado.edu/en/simulation/sound

Physics for Scientists and Engineers – An

Interactive Approach

Images: http://www.elateafrica.org/elate/physics/waves/formsofwavefronts.

htm

http://hyperphysics.phy-astr.gsu.edu/hbase/acoustic/invsqs.html

Works Cited