Question

2 questions thx

1) A point source emits sound waves isotropically. A sound meter measures a sound level of 51.72 dB at location C and a sound level of 45.53 at location D, a distance of 16 m from location C. The two locations C and D and the point source are all located along the same line. How far from location C is the point source? Give your answer in m, though enter only the numerical part in the box.

2) A point source emits sound waves isotropically. A sound meter measures a sound level of 51.21 dB at location C and a sound level of 47.79 at location D, a distance of 15 m from location C. The two locations C and D and the point source are all located along the same line. What is the total output power emitted by the point source? Give your answer in mW, though enter only the numerical part in the box.

Answer 1

1)
let beta1 = 51.72 dB
beta2 = 45.53 dB

let I1 and I2 are sound intensities at locations C and D.

we know,

beta1 = 10*log(I1/Io)
51.72 = 10*log(I1/10^-12)
5.172 = log(I1/10^-12)

10^5.172 = I1/10^-12

==> I1 = 10^(5.172 - 12)

I1 = 1.486*10^-7 W/m^2

simillarly,
I2 = 10^(4.553 - 12)

= 3.573*10^-8 W/m^2

let x is the distance from point source to location C.

now use,

I2/I1 = x^2/(x + 16)^2

3.573*10^-8/(1.486*10^-7) = x^2/(x + 16)^2

==> x = 15.6 m <<<<<<<<<<------------------Answer

2)

simillarly solution 1
I1 = 10^(5.121 - 12) = 1.321*10^-7 W/m^2
I2 = 10^(4.779 - 12) = 6.01*10^-8 W/m^2

let x is the distance from point source to location C.

now use,

I2/I1 = x^2/(x + 16)^2

6.01*10^-8/(1.321*10^-7) = x^2/(x + 15)^2

==> x = 31.1 m

so, I1 = P/(4*pi*x^2)

P = I1*4*pi*x^2

= 1.321*10^-7*4*pi*31.1^2

= 0.00161 W

= 1.61 mW <<<<<<<<<--------------------------Answer