Intensity I of a sound wave is defined as I = P/A and sound intensity level is d

Question

Intensity I of a sound wave is defined as I = P/A and sound intensity level is defined as beta = 10 log_10 (I/I_0) where I_0 is the intensity corresponding to the threshold of hearing. Assume that the source of sound is located in the exact center of a large sphere, so that the power of the sound wave is distributed evenly over the surface area A of the sphere. To the right are five scenarios where the power of the source (P) and the radius of the sphere (R) are given. Rank the sound intensity levels from highest to lowest. P = 1.20 times 10^2 W, R = 36.0 m P = 1.20 times 10^2 W, R = 12.0 m P = 3.60 times 10^2 W, R = 12.0 m P = 1.20 times 10^2 W, R = 4.00 m

Explanation / Answer

1. P = 1.20 x 10^2 W and R = 36 m

I = P/A = P / (4 pi R^2) = 7.368 x 10^-3 W/m^2

Sound LEvel = 10 log( I / 10^-12) = 98.7dB

2. P = 1.20 x 10^2 W and R = 12 m

I = P/A = P / (4 pi R^2) = 0.0663 W/m^2

Sound LEvel = 10 log( I / 10^-12) = 108.2 dB

3. P = 3.60 x 10^2 W and R = 12 m

I = P/A = P / (4 pi R^2) = 0.199 W/m^2

Sound LEvel = 10 log( I / 10^-12) = 113 dB

4.
P = 1.20 x 10^2 W and R = 4 m

I = P/A = P / (4 pi R^2) = 0.597 W/m^2

Sound LEvel = 10 log( I / 10^-12) = 117.8 dB

These are in increasing order.

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