A 15 W speaker emits sound waves in all directions equally. a) Calculate the sou

Question

A 15 W speaker emits sound waves in all directions equally.  

a) Calculate the sound intensity 10 m from the source. b)Calculate the sound level 10 m from the source. c)Calculate how many identical speakers are needed to produce a painfully loud sound (120dB) 10 m from the source. (Pain threshold is 1 W/m2)

Two speakers are driven by the same amplifier with a frequency of 1380 Hz. The two speakers are 4 m apart. An observer, originally at the position of one of the speakers, starts moving away along a line perpendicular to the line connecting the two speakers. The speed of sound in air = 345 m/s d)Calculate the number of sound minima the observer will hear while the observer is moving to a spot 3 m from the speaker.

Explanation / Answer

(A) I = P / (4 pi r^2)

= 15/ (4 x pi x 10^2)

= 0.0119 W/m^2

(B) Sound level = 10 log (I / I0)

=10 log (0.0119 / 10^-12)

= 100.8 dB  

(C) 120 = 10 log( I' / 10^-12)

I' = 1 W/m^2

n = I' / I = 84 speakers

(D) wavelength = v / f = 345 / 1380 = 0.25 m

when path difference = (2n + 1)(0.25/2)  

= (2n +_ 1) 0.125

n = 0, 1, 2 , 3 ,4 .....

x - (4 - x) = (2n + 1)(0.25/2)

x = 0.125 , 0.375, 0.625, .....

number of minima = 15 minima

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