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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: 2,427 Thanks: 1314 
$80dB + 80dB = 10\log_{10}(2) +80 dB = 83dB$

January 29th, 2018, 10:07 PM  #3 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3  
January 29th, 2018, 10:43 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314  Quote:
$A = 80dB = 10^8 A_0$ $A + A = 2 \times 10^8 A_0$ 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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