(a) Calculate the minimum safe distance you can be from a speaker that puts out

Question

(a) Calculate the minimum safe distance you can be from a speaker that puts out 2.40 W of sound, using the following assumptions: The sound power spreads uniformly over a sphere of radius r and area 4r2, your eardrum area is 0.900 cm2, and it cannot tolerate more than 1.00 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. m?

(b) 2.40 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)

Power from the speaker , P = 2.4 W

let the minimum safe distance fro speaker is d

area , A = 0.90 cm^2

Intensity = Power/area

2.4/(4 * pi * d^2) = 1 *10^-6/(0.9 *10^-4)

solving for d

d = 4.15 m

the minimum safe distance from the speaker is 4.15 m

b)

let the efficiency of speaker is u

efficiency = input power /output power

efficiency = 2.4/(100) * 100

efficiency = 2.4 %

the efficiency of this speaker in converting electrical power to sound is 2.4 %

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