Question

A point source is emitting sound in all directions. Find the
ratio of distance of two points from the point source where
the difference in loudness levels is 3 dB. (log10 2 = 0.3)
(1) 2
(B)3
(C) 1/2
(D) 1/2​

Answer 1

Answer:

The answer will be 1/√2

Explanation:

According to the problem there is a point source which emitting sound.

Now there are two points from the point source.

Now we know that loudness , β = 10 log I/I0

where I = K/r^2 means I is inversely proportional to r^2

Therefore,  β = 10 log  K/r^2/I0

                       =  10 log  K/r^2I0

                       = 10 { log k' - 2 log r}

As it is a constant statement we can write,

β1= 10 { log k' - 2 log r1}

β2= 10 { log k' - 2 log r2}

Now the difference in loudness is given as 3 dB

Therefore ,

β1 - β2 = 10 [ 2 log (r2/r1)]

=> 3 = 10 log (r2/r1)^2

=> 0.3 =  log (r2/r1)^2

=> 2 = (r2/r1)^2

Therefore , r1=r2 = 1 /√2