This document discusses sound waves, power, intensity, and how they relate to distance from a sound source. It provides equations for power and intensity of sound waves. Power is the rate at which energy is delivered, while intensity is the power delivered per unit area. Intensity is inversely proportional to the square of the distance from an isotropic (uniformly radiating) source. The document includes a sample problem asking how the amplitude of sound waves observed by a person would change if the distance from the speaker doubled. The solution is that the amplitude would halve, since intensity, and thus amplitude, is inversely proportional to the square of the distance.

1. Sound Waves
Power and Intensity
Physics 101 Learning Object

2. Power
 Power (P): the rate at which the wave delivers energy (in W)
Equation:
where
μ = linear mass density
ν = wave speed
ω = angular frequency
A = amplitude of wave

3. Intensity
 Intensity (I): the power delivered per unit area (in W/m^2)
Equation:
where
ρ = density of the medium
ν = wave speed
ω = angular frequency
A = amplitude of wave

4. Isotropic Power and Intensity
 Isotropic: uniform in all directions (when a source is
enclose in a spherical surface)
 Since power is radiated isotropically by a source, then the
intensity must be equal in all surface area. Therefore:
 Rearrange:

5. Target Problem
A person is standing beside a speaker as it plays 10,000 Hz tone.
The sound waves travels 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) Decrease by a factor greater than 2 but less than 4
b) Halves
c) Doesn’t change
d) Decrease by a factor of 8
e) Decrease by less than half
f) Decrease by a factor of 4

6. Key Words in the Problem
A person is standing beside a speaker as it plays 10,000 Hz
tone. The sound waves travels 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:
 UNIFORMLY = isotropically
 distance from speaker DOUBLES = r -> 2r
 AMPLITUDE = what we want to find

7. Solution
Since the question tells us that the sound waves travels
uniformly, we immediately know that we should use:
Since we want to know whether r will affect the
amplitude, we isolate the A and the r by setting the two
Intensity equations equal to each other:

8. Solution Cont’d
Then, we isolate A and r:

9. Solution Cont’d
As we can see in this equation, only 1/r affects the amplitude.
If we double the r, the equation becomes:
and we can compare the two equations discovering that the
difference of amplitude only differs by half of the remaining
equation. Therefore, the answer is B, the amplitude halves.

10. Key Concept
The key concept of this problem is that the intensity of a
sound source radiated isotropically is inversely
proportional to the square of the distance from the source:
Therefore, if we substitute the amplitude from another
intensity question, we can find out the relationship
between the amplitude and the distance:

11. Common Mistake
A common mistake is that students will use the power
equation to solve for this question.
But why can’t we use the power equation?
If we use common sense to think about this question, we
know that power never changes, but intensity will change
as the distance differs. The further the distance, the
smaller the intensity. Therefore, we know not to use the
power equation to solve this question because we need a
variable (or several variables in this case) that will not
change to find out the relationship/ ratio of the amplitude
and the radius.