Suppose that a duck quacks at a frequency of 486 Hz and with an intensity of 1.5

Question

Suppose that a duck quacks at a frequency of 486 Hz and with an intensity of 1.50 x 10^ -7 W/m^2. What is the sound intensity level of one quacking duck? What is the sound intensity level of five quacking ducks? Suppose that two ducks are separated by a distance of 3.64 m and are quacking in phase. If you are 2.80 m in front of one duck, will you hear constructive or destructive interference?

The answers are as follows. I just need to know how to get these answers.

a) B1= 52dB B2

B) B5= 59db

C) The waves are out of phase by a half wavelength, so you will hear destructive interference.

Explanation / Answer

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

I0 = 10^-12 W/m^2

I=1.50*10^-7 W/m^2

Plugging given data,

I=10*log[(10^-7)/(10^-12)]

I=10*log[10^5]

I= 50dB…………………..For one duck

I=10*log[(5*10^-7)/(10^-12)]

I=10*log[5*10^5]

I= 57 dB ……………………For five ducks

wavelength = v/f = 343/486 = 0.7057

Path length = L= L1- L2

L= 2.80 – (3.64-2.80)

L= 1.96m

Phase difference = (2/)*path difference

Phase difference = (2/0.7057)*1.96 = 17.45

Hence we will hear constructive interference.

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