Sound Intensity Practice Problems

Sound intensity is the pressure per unit of area of a sound wave. It can be calculated using the power output of a source and how far the listener is from that source.

Sound Intensity

$\large\mathsf{ I = \frac{P}{A} = \frac{P}{4 \pi r^2} }$

Use the intensity equation to solve these problems on your own. Check your work when you are done.

Problem	Given/Find	Equation	Solution
An amplifier has a power output max of 2.0 W. If you are standing 2.0 meters away from that speaker, what is the sound intensity at that distance at max output?	$\mathsf{ P = 2.0 \text{ W}}$ $\mathsf{ r = 2.0 \text{ m} }$ $\mathsf{ I = ? \text { W/m}^2 }$	$\mathsf{ I = \frac{P}{4 \pi r^2} }$	$\mathsf{ I = \frac{2.0 \text{ W}}{4 \pi (2.0 \text{ m})^2} }$ $\mathsf{ I = 0.040 \text{ W/m}^2 }$
An umpire yells "strike" when a baseball player misses the ball. His power output is 3.16 x 10^-2 W. What intensity does the player hear the umpire if he is standing 1.00 m away?	$\mathsf{ P = 3.16 \times 10^{-2} \text{ W}}$ $\mathsf{ r = 1.00 \text{ m} }$ $\mathsf{ I = ? \text { W/m}^2 }$	$\mathsf{ I = \frac{P}{4 \pi r^2} }$	$\mathsf{ I = \frac{3.16 \times 10^{-2} \text{ W}}{4 \pi (1.00 \text{ m})^2} }$ $\mathsf{ I = 0.00251 \text{ W/m}^2 }$
To a listener that is 25.0 meters away from the platform, hears a symphony orchestra with an intensity of 8.91 x 10^-3 W/m². What is the power output of that symphony?	$\mathsf{ P = ? \text{ W}}$ $\mathsf{ r = 25.0 \text{ m} }$ $\mathsf{ I = 8.91 \times 10^{-3} \text { W/m}^2 }$	$\mathsf{ I = \frac{P}{4 \pi r^2} }$	$\mathsf{ 8.91 \times 10^{-3} \text { W/m}^2 = \frac{P}{4 \pi (25.0 \text{ m})^2} }$ $\mathsf{ P = (8.91 \times 10^{-3} \text { W/m}^2)(4 \pi (25.0 \text{ m})^2) }$ $\mathsf{ P = 70.0 \text{ W} }$

Can you solve these sound intensity problems?