Question

The intensity levels of two people's speech are 62.5 dB and 65.5 dB, respectively. What is the intensity level of the combined sounds?

Answer 1

let

beta1 = 62.5 dB
beta2 = 65.5 dB

let I1 and I2 are the intensity of the sound produced by the two people.

beta1 = 10*lg(I1/Io)

62.5 = 10*log(I1/10^-12)

6.25 = log(I1/10^-12)

10^6.25 = I1/10^-12

I1 = 10^(6.25 - 12)

I1 = 1.778*10^-6 W/m^2

simillary

beta2 = 10*lg(I2/Io)

65.5 = 10*log(I2/10^-12)

6.55 = log(I2/10^-12)

10^6.55 = I2/10^-12

I2 = 10^(6.55 - 12)

I2 = 3.548*10^-6 W/m^2

Intensity of ambined sound, I = I1 + I2

= (1.778 + 3.548)*10^-6

= 5.326*10^-6 W/m^2

the intensity level of the combined sounds,

beta = 10*log(I/Io)

= 10*log(5.326*10^-6/10^-12)

= 67.3 dB <<<<<<<<<<<----------------------Answer