An Intense Car Stereo

Part A = 4.8
Part B = 2.1
Part C = 13.8
Part D = 1.38*10⁵
Solutions Below:

A popular car stereo has four speakers, each rated at 60 W. In answering the following questions, assume that the speakers produce sound at their maximum power.

Part A

Find the intensity I of the sound waves produced by one 60 W speaker at a distance of 1.0 m.
Express your answer numerically in watts per square meter. Use two significant figures.

Intensity is given by the formula:
I = P/A
Where P is power and A is area of the surface receiving the sound (generally this will be the shape of a sphere, 4πr².
I = 60/(4πr²)
I = 60 / (12.56636(1)²)
I = 4.8 W/m²


Part B

Find the intensity I of the sound waves produced by one 60 W speaker at a distance of 1.5 m.
Express your answer numerically in watts per square meter. Use two significant figures.

Using the same formula as in Part A:
I = 60/(4πr²)
I = 60 / (12.56636(1.5)²)
I = 2.1 W/m²


Part C

Find the intensity I of the sound waves produced by four 60 W speakers as heard by the driver. Assume that the driver is located 1.0 m from each of the two front speakers and 1.5 m from each of the two rear speakers.

Express your answer numerically in watts per square meter. Use two significant figures.
Just add up the intensities from Parts A and B. 2 speakers at 1.0m = 2 * 4.8 and 2 speakers at 1.5m = 2 * 2.1. So:
I = (2 * 4.8) + (2 * 2.1)
I = 13.8 W/m²


Part D

The threshold of hearing is defined as the minimum discernible intensity of the sound. It is approximately 10^-12 W/m^2. Find the distance d from the car at which the sound from the stereo can still be discerned. Assume that the windows are rolled down and that each speaker actually produces 0.06 W of sound, as suggested in the last follow-up comment.

Express your answer numerically in meters.
Since I = P / A and A = 4πr²:
I = P / 4πr²
10^-12 = (0.06 * 4 speakers) / (12.56636r²)
10^-12 = 0.019099r²
r² = 19098609303
r = 138198m
Or in scientific notation:
r = 1.38*10⁵m