Question

A certain siren radiates sound uniformly in all directions. At a distance of 17 m from the siren, the intensity level is 49 db. How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10-12 W/m2.

Answer 1

The power is
`P = 2.88*10^(-4 ) \ W`

Step-by-step explanation:

From the question we are told that

The distance from the siren is
`d = 17 \ m`

The intensity level is
`\beta = 49\ dB`

The threshold of hearing is
`I_0 = 1.0 *10^(-12) \ W/m^2`

Generally the intensity level is mathematically represented as

`\beta = 10dB * log [(I)/(I_o) ]`

Where I is the intensity at which the siren radiates the sound

substituting values

`49 = 10 * log [(I)/(1.0 *10^(-12)) ]`

=>
`I = 7.94*10^(-8) W/m^2`

Now the amount of power the siren put out is mathematically evaluated as

`P= IA`

Where A is the area of the siren which is taken as a sphere and it is mathematically evaluated as

`A = 4 \pi d^2`

So

`P = I * 4 \pi d^2`

substituting values

`P = 7.94 *10^(-8) * 4 * 3.142 * (17)^2`

`P = 2.88*10^(-4 ) \ W`