The sound intensity level due to a barking dog at a distance 2 m from the dog is 90 dB.

A) What is the intensity ( I ) in Watt/m² of sound at a distance 2 m from the dog?

B) What is the sound power ( P ) in Watt produced by the dog's vocal cords. Assume that the sound power produced by the dog's vocal cords is distributed uniformly in all direction.

 

Question A

The sound decibel scale is defined mathematically as

dB = 10 log (I/Io)

I is the intensity of sound which is unknown

Io is the default sound intensity which is 1*10^-12 w/m^2

dB is the decibel of sound which is 90dB

By substituting the parameters, we have that

90 = 10 log (I/1*10^-12)

90/10 = log (I/1*10^-12)

9 = log (I/1*10^-12)

10^9 = (I/1*10^-12)

I = 10^9 * 1*10^12

I = 0.001 w/m^2

Intensity of sound at a distance of 2m from the dog is 0.001 w/m^2

Question 2

Sound power = intensity * area

Assuming a spherical region, the area of the surface is

Area = πr^2

Area = 3.142 * 2^2

Area = 12.566 m^2

Sound power = 0.001 * 12.566 = 0.0126W

Sound power is 0.0126W