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April 17th, 2017, 12:50 AM  #1 
Senior Member Joined: Apr 2008 Posts: 193 Thanks: 3  Is the answer wrong for this problem about sound intensity?
I am going to write down a sentence below. (ex) What is the approximate combined loudness in decibels of a garbage disposal truck and a washing machine, each with a sound intensity of 80 decibels? It looks like a simple problem. I thought the answer was 160 decibels. I got that by multiplying 80 by 2 since the two sounds have the same intensity. But, the answer key says 83 decibels. Is the answer key wrong? Please give me your comments. Thanks. 
April 17th, 2017, 04:12 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,107 Thanks: 1907 
The number of decibels is logarithmic. "multiplying by 2" is represented by adding 10log$_{10}$(2), which is 3.010..., giving 83.0 to 3 significant figures.

April 22nd, 2017, 10:48 AM  #4 
Senior Member Joined: Apr 2008 Posts: 193 Thanks: 3 
Thanks for the link, Joppy.


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