Question

The intensity ,I from a point source decreases with the inverse square of the distance,r from the source.Suppose that you are listening to your favourite music coming away from a speaker(regarded as a point source and in an open area) placed exactly r1 from you.then you suddenly decide to move away to a new position ,r2 which is exactly twice as far away from the speaker.

Calculate by how many decibels ,dB does the sound intensity level ,β drop ,when you move twice as far away from the speaker to your new position.

Answer 1

The intensity in decibels is written as,

Here I0 is the reference intensity for the decibel scale and I is the intensity. Since the intensity is proportional to the inverse square of the distance, we can write,

k is a constant.

We can write the intensities I1 and I2 as,

r2 is two times r1 substituting we get,

Hence the difference between the intensities is,

Therefore the intensity drops by 6.02 decibels.