Sound Intensity Formula with Sample Problems

Sound Intensity Formula :

Sound intensity I (db) in decibel is equal to the product of the sound power P(w) in watt is divided by the area A(m2) in meter square. Hence the sound intensity formula has been written as,

I (db) = P(w)  / A(m2)


P → sound power in w

A → area in m2

In order to measure the sound intensity level, need to compare the given sound intensity value with standard intensity value.

The formula of Sound Intensity Level is expressed as,

IL= 10 log10 I /I0


I → sound intensity in db

Io → reference intensity in w/m2

The unit of sound intensity is expressed in decibels (dB)

Sample Problems :

Problem1 :

Calculate the sound intensity at a distance of 10m? In a person whistles with the power of 2 * 10-4 W.

Solution :


P (power) = 2*10-4

A (here distance) = 10 m

So by using the sound intensity formula,

I = P / A

I = 2*10-4 / 10

I = 2*10-5

Thus the sound intensity in this condition will be 2*10-5W/m2.

Problem2 :

What is the level of sound sensation in decibels corresponding to an intensity wave 10-10 W/m-2?

Solution :

The first thing to notice is that they are already giving us the intensity of sound, so we can easily calculate the sound sensation.

I = 10-10 W/m-2.

S = 10*log(I/I0)

= 10*log(10-10W/m-2/0-12 W/m-2)

= 20 dB

S = 20 dB.

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