A loudspeaker at a lifeguard station on a Pacific ocean beach emits sound with e

Question

A loudspeaker at a lifeguard station on a Pacific ocean beach emits sound with equal intensity in all directions. At 10.00 m from the source, die sound level measured is 100 dB. (a) What is the intensity of the sound in W/m^2 at this distance? (b) What is the intensity (W/m^2) of the sound at the surface of the seawater 25.0 m from the source? (c) How much power is transmitted to the eardrum (area = 8 times 10^-5 m^2) of a swimmer at the surface at this location? (d) The sound passes from the air into the water where it continues to propagate. Using the constants given at the top of this page, calculate the acoustic impedance in air and in seawater. (e) What percentage of the sound's intensity is (i) reflected (ii) transmitted at the water surface? (f) The swimmer in (c) dives to 2.00 m below the water surface. What is die intensity (W/m^2) and sound level (dB) of the sound at this position?

Explanation / Answer

a)

using the equation

dB = 10 log10(I/Io)

100 = 10 log10(I/10-12)

I = 0.01 W/m2

b)

I1 = 0.01 , r1 = 10 m

I2 = ?   , r2 = 25 m

using the equation

I1/I2 = r22/r12

0.01/I2 = (25/10)2

I2 = 0.0016 W/m2

c)

P= power trasmitted = I2 A = (0.0016) (8 x 10-5) = 1.28 x 10-7 watt

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