Sound Intensity: Reduce by 35 dB, Factor Calculation

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Homework Help Overview

The discussion revolves around calculating the factor by which sound intensity is reduced when the sound intensity level is decreased by 35 dB. The subject area includes concepts of sound intensity and logarithmic relationships in acoustics.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants attempt to apply the formula Δβ=10Log(I/I°) to find the factor of reduction. There are questions about the correctness of their calculations and the interpretation of the results.

Discussion Status

Some participants express confusion over the calculations and seek clarification on the steps involved in solving for the intensity ratio I/I°. There is an ongoing exploration of different interpretations of the results, with no explicit consensus reached.

Contextual Notes

Participants note that the original calculations may not align with expected outcomes, and there is discussion about how to express the final answer regarding the factor of reduction.

Faraz
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Homework Statement


If you install special sound-reflecting windows that reduce the sound intensity level by 35.0 dB , by what factor have you reduced the sound intensity?

Homework Equations


Δβ=10Log(I/I°)

The Attempt at a Solution


I°=10^-12
I=I°-35
35=10^1.5440680
(I/I°)={(10^-12)-(10^1.5440680)}/{10^-12} =-3.5*10^13
But this is wrong
 
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Faraz said:

Homework Statement


If you install special sound-reflecting windows that reduce the sound intensity level by 35.0 dB , by what factor have you reduced the sound intensity?

Homework Equations


Δβ=10Log(I/I°)

The Attempt at a Solution


I°=10^-12
I=I°-35
35=10^1.5440680
(I/I°)={(10^-12)-(10^1.5440680)}/{10^-12} =-3.5*10^13
But this is wrong

Welcome to the PF.

I didn't follow some of what you did. Instead, start with substituting the -35dB into your first Relevant Equation:

-35dB=10Log(I/I°)

Now show the steps you use to solve for the fraction I/Io... :smile:
 
-3.5=log(I/I°)
10^-3.5=(I/I°)
but still wrong
 
Faraz said:
-3.5=log(I/I°)
10^-3.5=(I/I°)
but still wrong

It should be right, IMO. Do you get about 1/3162 as the answer?
 
Maybe the answer is supposed to be stated as "reducing the sound intensity by a factor of 3162..."?
 

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