Question

A bystander observes the musicians heading toward each other. When musician #1 is 100 m away, the intensity is 1.24 x 10-8 W/m^2. What is the intensity AND intensity level when musician #1 is 25 m away?

Answer 1

Step-by-step explanation:

Given that,

Distance 1, r = 100 m

Intensity,
`I_1=1.24* 10^(-8)\ W/m^2`

If distance 2, r' = 25 m

We need to find the intensity and the intensity level at 25 meters. Intensity and a distance r is given by :

`I=(P)/(4\pi r^2)`.........(1)

Let I' is the intensity at r'. So,

`I'=(P)/(4\pi r'^2)`............(2)

From equation (1) and (2) :

`I'=(Ir)/(r'^2)`

`I'=(1.24* 10^(-8)* 100)/(25^2)`

`I'=1.98* 10^(-9)\ W/m^2`

Intensity level is given by :

`dB=10\ log((I')/(I_o))`,
`I_o=10^(-12)\ W/m^2`

`dB=10\ log((1.98* 10^(-9))/(10^(-12)))`

dB = 32.96 dB

Hence, this is the required solution.