Is the answer wrong for this problem about sound intensity?

Apr 2008
194
3
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.
 

skipjack

Forum Staff
Dec 2006
21,478
2,470
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.
 
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Feb 2016
1,849
657
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That answer seems correct.

Take a look at this, a nice walk through.
 
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