Question

You hear a mosquito buzzing from a distance d= 3.4 m from your ear. You hear a sound intensity level of 65.5 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.

Question was previously answered but not understood, can you please include how you compute the numbers with powers of multiplication on a calculator.

Answer 1

First, we need to find the intensity using the given sound level

L = 10 log_e ( I / I_o )

L is given sound level in dB

where, I_o = 1e-12 W/m² ( threshold frequency)

so,

65.5 = 10 log_e ( I / I_o )

65.5 / 10 =  log_e ( I / I_o )

Now , whenever you see log_e , it means exponential of 10, this means

10^65.5/10 = I / I_o

10^6.55 = I / I_o

3.548e6 = I / I_o

3.548e6 = I / 1e-12

I = 3.548e6 * 1e-12

I = 3.548e-6 W/m²

Now,

we know

I = P / A

as waves are spherical, we have

I = p / 4r²

P = I * 4r²

P = 3.548e-6 * 4 * 3.4²

P = 5.2e-4 W