Intensity level at a distance 200 cm from a point source of sound is 80 dB. If there is it loss of acoustic power in air and intensity of threshold hearing is `10^-12` W`m^-2`, then the intensity level at a distance of 4000 cm from source is (log 20 = 1.3)

Options

A. Zero
B. 54 dB
C. 64 dB
D. 44 dB

Answer

B

Explanation

Intensity `(I)prop(1)/(r^(2))`
`implies (I_(2))/(I_(1))=(|r_(1)^(2))/(r_(2)^(2))=(2^(2))/((40)^(2))=(1)/(400)`
`implies I_(1)=400I_(2)`
`L_(1)=10log_(10)((I_(1))/(I_(0)))`
`L_(2)=10log_(10)((I_(2))/(I_(0)))`
`implies L_(1)-L_(2)=10log((I_(1))/(I_(2)))=10log_(10)(400)`
`implies L_(1)-L_(2)=10xx2.602=26dB`
`implies L_(2)=L_(1)-26=80-26=54dB`