Police Car Sound Intensity Change

[JumpinJohny]

Homework Statement

A police siren produces a sound whose frequency range from 635Hz to 912Hz. When the police car is 220 meters from from the scene of an accident, the sirens blare at 75dB. How many decibels higher will the sound intensity be when the police car is 55m away?

Homework Equations

The sound intensity = A^2*f^2, but I'm not sure if I am missing something there.

The Attempt at a Solution

If that equation is right, then I'd use ((220^2)(f^2))-((55^2)(f^2)); I'm stuck after that

 

[Mthees08]

well I am not 100% sure on how to solve this either, but we know the sound is expanding as a shell. As that shell expands it will become less and less intense. and we set up an equation where Intensity2/intensity1=radius1^2/radius2^2 based the equation [4(pi)r^2]^-1=I

also make sure to convert from dB into W/m^2

 

[JumpinJohny]

Do you know what that conversion is?

 

[flatmaster]

I know dB is a logarythmic, rather than a linear scale, so be carefull of that. I'm not sure if it's base 2 log or something else.

 

[Mthees08]

10dbxlog(base10)([intensity in W/m^2]/[1.0E^-12w/M^2]=Intensity in Db

so somebody needs to rearrange that but I can't do all the work.., ok maybe I will.

I/10=log(I/1.0E^-12)
e^(I/10)=I/1.0E^-12
1.0E-12e^(I/10)=Intensity in W/m^2