Question

What is the sound intensity of a whisper at a distance of 2.0 m, in W/m²? What is the corresponding sound intensity level in dB?

Answer 1

To solve this problem we apply the concepts related to the Intensity, which is defined as the Power given by the object on unit area. Mathematically this is,

$I = \frac{P}{A}$

Where,

I = Intensity

P = Power

A = Area

Considering that a whisper is around to $1*10^{-10}W$, then we have that

$I = \frac{1*10^{-10}}{2^2}$

$I = 2.5*10^{-11} W/m^2$

Intensity level in

$\beta = 10log (\frac{I}{I_0})$

Where,

$I_0 =$ Threshold intensity level

$\beta = 10log (\frac{2.5*10^{-11}}{1*10^{-12}})$

$\beta = 14dB$

Therefore the corresponding sound intensity level  is 14dB