(a) Calculate the minimum safe distance you can be from a speaker that puts out
ID: 1315820 • Letter: #
Question
(a) Calculate the minimum safe distance 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?r2, 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) 2.00 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?
% (a) Calculate the minimum safe distance 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?r2, 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) 2.00 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
Answer
a) The minium distance of sound is 1 W/m^2
So I = P/A or
A = P/I = 6.35W/1W/m^2 = 6.35m^2
Now 4?*r^2 = 6.35
So
r = sqrt(6.35/4?) = 0.505m = 5.05 x 10^(-5) km
b) The threshold of sound is 1.0x10^-12W/m^2
So I = P/A or
A = P/I = 6.35W/(1.0x10^-12W/m^2) = 6.35x10^12m^2
Now 4?*r^2 = 6.35x10^12
So r = sqrt(6.35x10^12/4?) = 7.10x10^5m = 7.10 x 10^2 km
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