Question

Harry and Sally are sitting on opposite sides of a circus tent when an elephant trumpets a loud blast. If Harry experiences a sound intensity level of 65 dB and Sally experiences only 49 dB, what is the ratio of the distance between Sally and the elephant to the distance between Harry and the elephant

Answer 1

Intensity is given by:

I = Pav/A = Pav/(4*pi*r^2)

Sound level is given by:

SL = 10*log (I/I0)

Sound level at Harry's location will be

SLh = 10*log (Ih/I0)

Sound level at Sally's location will be

SLs = 10*log (Is/I0)

difference between sound level at both location is given by:

SLh - SLs = 10*log (Ih/I0) - 10*log (Is/I0)

Using logarithm property

65 - 49 = 10*log (Ih/Is)

Since power source is same for both Harry and Sally, So

Ih/Is = (rs/rh)^2

16 = 10*log (rs/rh)^2

16 = 20*log (rs/rh)

log (rs/rh) = 4/5

rs/rh = 10^(0.8)

rs/rh = 6.31

rs : rh = 6.31 : 1