Police Car Sound Intensity Change

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Homework Help Overview

The problem involves calculating the change in sound intensity of a police siren as the distance from the source changes. The frequency range of the siren is given, along with the initial sound intensity level at a specific distance.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between sound intensity and distance, referencing the concept of sound expanding as a shell. They mention using an equation relating intensity and distance, but there is uncertainty about the correct approach and necessary conversions.

Discussion Status

There is an ongoing exploration of the mathematical relationships involved, with some participants suggesting equations and conversions needed to solve the problem. However, no consensus has been reached on the method to use, and multiple interpretations of the problem are being considered.

Contextual Notes

Participants note the need to convert sound intensity levels from decibels to watts per square meter, and there is a caution about the logarithmic nature of the decibel scale. Some assumptions about the equations and their application are being questioned.

JumpinJohny
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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 :frown:
 
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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
 
Do you know what that conversion is?
 
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.
 
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
 

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