My Math Forum Is the answer wrong for this problem about sound intensity?

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 April 16th, 2017, 11:50 PM #1 Senior Member   Joined: Apr 2008 Posts: 194 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, 03:12 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,381 Thanks: 2011 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. Thanks from davedave
 April 17th, 2017, 03:15 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,770 Thanks: 627 Math Focus: Yet to find out. That answer seems correct. Take a look at this, a nice walk through. Thanks from davedave
 April 22nd, 2017, 09:48 AM #4 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 Thanks for the link, Joppy.

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