How to find the total dB of two sounds?

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Homework Help Overview

The problem involves calculating the total loudness in decibels (dB) when two sound sources of the same frequency are active, given that one source produces a loudness of 70dB when alone. The context is within acoustics and sound intensity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between amplitude and intensity, questioning the use of square roots in the calculations. There is an exploration of how intensity relates to amplitude and how this affects the dB calculation.

Discussion Status

Some participants are clarifying the mathematical relationships involved in the problem, particularly regarding the definitions of intensity and amplitude. There is an acknowledgment of differing interpretations of the equations used, but no consensus has been reached on the correct approach.

Contextual Notes

Participants are grappling with the definitions and relationships between amplitude, intensity, and their representation in decibels. There is a noted confusion regarding the correct application of these concepts in the context of the problem.

Summer95
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Homework Statement


The frequency of the two sounds is the same, and the observer is equal distance from either sound source. When one speaker is turned off the loudness is 70dB, what is the total loudness when it is turned back on?

Homework Equations


A2∝I
dB=10log(I/I0)

The Attempt at a Solution


$$10log(\sqrt{\frac{2A}{A}})=10log\sqrt{2}=1.5$$
and 70+1.5=71.5dB

but I do not see it done this way anywhere so I don't know what I'm doing wrong
 
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Intensity is amplitude squared, not the other way round. Where does the square root come from?
 
The square root comes from the equation for dB which is 10log(I/I0)

But if you are doubling the amplitude that part becomes √2 right?
 
Summer95 said:
The square root comes from the equation for dB which is 10log(I/I0)

But if you are doubling the amplitude that part becomes √2 right?
because Intensity is proportional to the root of amplitude.
 
Summer95 said:
because Intensity is proportional to the root of amplitude.
nevermind your right I had it the wrong way round
 

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