The electrical power needed to operate a speaker in your audio system is 24.7 W.

Question

The electrical power needed to operate a speaker in your audio system is 24.7 W. If this speaker has a circular opening with a radius of 0.0823 m and the average sound intensity at the opening is 20.1 W/m^2, determine the ratio of sound output power P_sound to electrical input power P_electrical. Sound is emitted by a point source. You wish to compare the sound intensity and sound intensity level from this source at two different sites. If the distance to the second site is a factor of 8 greater than the distance to the first, determine the following. (a) Determine the multiplicative factor by which the sound intensity decreases as you go from the first to the second site. (Assume the intensities at the first and second sites are I_1 and I_2, respectively.) (b) Determine the additive amount by which the sound level intensity decreases as you go from the first to the second site. (Assume the sound level intensities at the first and second sites are beta_1 and beta_2, respectively.)

Explanation / Answer

Pelectrical = 24.7 W

Intensity = Powe/area

Psound = 20.1*3.14*0.0823^2

Psound/pelectrical = 20.1*3.14*0.0823^2/24.7

= 0.0173

d2 = 8d1

(a) I = powe/ area

I1/I2 = d2^2/d1^2

I1/I2 = 64

(b) Beta = 10 log(I1/Io)

B1 -B2 = 10 log(64)

B1 - B2 = 18.1 dB

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