Math Is Fun Forum

davidtrinh

Member

Registered: 2016-12-03

Posts: 10

Is the answer wrong for this problem about sound intensity?

I am going to write down a problem 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 wrong? Please give me your comments. Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Is the answer wrong for this problem about sound intensity?

Hi;

I have two very loud air conditioners from the two zombies who live next door to me and require air conditioning when the outside temperature is 51 F. I guess they have to keep their skin from rotting off their already ugly faces...

I needed to know the intensity of the noise they were producing. I got it from these two sites

http://www.engineeringtoolbox.com/addin … -d_63.html

https://noisemeters.com/apps/db-calculator.asp

If you use their calculator you will see the book answer is correct.

They appear to be using this formula:

with

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Is the answer wrong for this problem about sound intensity?

hi davidtrinh

The decibel scale is logarithmic** so to add two sounds you need to 'anti-log' the amounts then re-log the result.

https://en.wikipedia.org/wiki/Decibel

decibel is one tenth of a bel so you need to convert first:

80 db = 8 b

so compute 10*log(10^8 + 10^8)

This comes out as 83 db

** so if the db goes up by +10 the sound is 10 times as loud.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

davidtrinh

Member

Registered: 2016-12-03

Posts: 10

Re: Is the answer wrong for this problem about sound intensity?

Thank you very much, bobbym and bob bundy.