16-1 Calculate the minimum safe distance (in m) you can be from a speaker that p

Question

16-1

Calculate the minimum safe distance (in m) you can be from a speaker that puts out 2.00 W of sound, using the following assumptions. The sound power spreads uniformly over a sphere of radius r and area 4 pi r^2, your eardrum area is 0.740 cm^2, and it cannot tolerate more than 1.00 times 10^-6 W. Damage is done by this small amount of power after prolonged exposure and can be repaired by the body, but damage done by 10^-4 W (found at many rock concerts) occurs almost instantaneously and prolonged exposure at that level produces permanent damage. (b) 2.00 W of sound power is very large compared to what the ear can tolerate. Suppose that 100 W of electrical power input (a typical value for many sound systems) is applied to this speaker. What is the efficiency of this speaker in converting electrical power to sound?

Explanation / Answer

a) P = 2.00 W, A = 0.740 cm2

I = P / A

2.0 / (4 pi d2) = 1.00 * 10-6 / (0.740 * 10-4)

d = 3.43 m

b) Efficiency = [2.00 / 100 W] * 100

Efficiency of speaker converting electrical power to sound = 2.0%

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