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April 17th, 2017, 12:50 AM   #1
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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.
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April 17th, 2017, 04:12 AM   #2
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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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April 17th, 2017, 04:15 AM   #3
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That answer seems correct.

Take a look at this, a nice walk through.
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April 22nd, 2017, 10:48 AM   #4
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Thanks for the link, Joppy.
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