Question

You hear a mosquito buzzing from a distance d= 3.2 m from your ear. You hear a sound intensity level of 68.9 dB.

Calculate the power of the sound being emitted by the mosquito, assuming it is a spherical emitter of sound. Use microwatts (μW) and 2 sf in your answer.

Answer 1

Sound level intensity is given by:

SL = 10*log (I/I0)

I0 = 10^-12 W/m^2 = Human threshold Intensity

given that SL = 68.9 dB

68.9 = 10*log (I/I0)

I/I0 = 10^(6.89)

I = 10^-12*10^(6.89)

I = 7.76*10^-6 W/m^2

Now relation between power and Intensity is given by:

P = I*A

P = I*4*pi*R^2

P = 7.76*10^-6*4*pi*3.2^2 = 998.55*10^-6 W

P = 998.55*10^-6 W = 998.55 W

In two significant figures

P = 1000 W = 1.0*10^3 W

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