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 January 29th, 2018, 06:53 PM #1 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 Is the key answer wrong? (ex) What is the approximate combined loudness in decibels of a garbage disposal and a washing machine, each with a sound level of 80 decibels? my attempt I use the formula. D = 10*log(I1/I2) where D represents the loudness of sound, I1 the intensity of source 1 and I2 the intensity of source 2. The two sounds have a combined loudness of 160 decibels. So, D=10*log(160) = 22 decibels. But the answer key says 83 decibels. Do you think it's wrong? Thanks for your help.
 January 29th, 2018, 06:58 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 $80dB + 80dB = 10\log_{10}(2) +80 dB = 83dB$
January 29th, 2018, 10:07 PM   #3
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Quote:
 Originally Posted by romsek $80dB + 80dB = 10\log_{10}(2) +80 dB = 83dB$
romsek, why did you change the first 80dB to the log value, but not the second 80dB?

Can you explain that? Thanks again.

January 29th, 2018, 10:43 PM   #4
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Quote:
 Originally Posted by davedave romsek, why did you change the first 80dB to the log value, but not the second 80dB? Can you explain that? Thanks again.
ok... signals in linear units will add.

$A = 80dB = 10^8 A_0$

$A + A = 2 \times 10^8 A_0$

now we convert to dB

\begin{align*} &10 \log\left(\dfrac{2 \times 10^8 A_0}{A_0}\right) = \\ \\ &10 \log(2\times 10^8) = 10(\log(2) + 8) = 80 + 10\log(2) \end{align*}

 January 30th, 2018, 10:47 PM #5 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 Thank you very much, romsek.

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