Question

A point source of sound emits a constant power with intensity inversely proportinal to the square of the distance from the source . By how many decible does the sound intensity level drops when you move from point P_(1) to P_(2) ? Distance of P_(2) from the source is two times the distance of source from P_(1) .

Answer 1

Hence the value of distance between two points is β2 − β1 = − 6.0 dB

Explanation:

we label the two points 1 and 2, and we use the equation β = 10 log I / I0(dB) twice. The difference in sound intensity level β2−β1 is given by

β2 − β1 = (10 dB)(log. I2 /I0 − log . I1 / I0)

(10 dB) [(log I2  − log I0) − (logI1−logI0)]  

= (10 dB) log. I2 / I1

Now, I ∝ 1r^2

⇒∴I2 / I1 = (r1 / r2)^2 = 1 / 4 asr2 = 2r1

β2 − β1 = (10 dB) log(1 / 4)

β2 − β1 = − 6.0 dB

Hence the value of distance between two points is β2 − β1 = − 6.0 dB