In the afternoon decibel level of a bus freeway is 100 dB wi

In the afternoon, decibel level of a bus freeway is 100 dB with 100 cars passing a given the every minute. Late at night, the traffic flow is only 20 cars per minute. What is the late-night decibel level? a. 20 dB b. 50 dB c. 80 dB d. 88 dB e. 93 dB

Solution

For 100 cars every minute,

Intensity in dB = 10 log(I_1/I_0) = 100 -------------------(i)

I_1 = I_0*10^10

For 20 cars every minute,

I_2 = (20/100)*I_1

I_2 = I_1/5 = 0.2*I_0*10^10

Intensity in dB = 10 log(I_2/I_0) = 10 log(0.2*I_0*10^10/I_0)

= 10( log(2) + 9) = 90+ 10*0.3 = 93 dB