# Decibel questions, how many people are cheering

## Homework Statement

In a neighborhood challenge to see who can climb a tree the fastest, you are ready to climb. Your friends have surrounded you in a circle as a cheering section; each individual alone would cause a sound intensity level of 80 dB at your location. If the actual sound level at your location is 87 dB, how many people are rooting for you?

Not a clue.

## The Attempt at a Solution

The book reads 5 as the answer, how would we get this though?

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Do you understand what a decibel (or even, a bel) is?

Yes, but without actually using the logs or taking the reverse of a log to get the answer, would there be a easier way to get it. i am just looking for the way to get the answer!!!!

BEL= log base 10 I/Io
DECIBEL= 10log base 10 I/Io

... Now... how would i obtain the answer?

mgb_phys
Homework Helper
You don't actually need logs ( assuming you have a calculator that can do powers)
You are looking for the ratio between the intensity of one person and the intensity from N people, dBs are designed to make it easy to do this calculation.

You know db = 10 log I/Io so I/Io = 10 ^ ( db/10)

Right, but I guess what I'm trying to say, is there a way or equation that adds a specific amount of decibels onto the original amount if they are all at the same amount of decibels.

like for instance 5 people at 80 decibels comes out to 87 decibels. how would i get the 5?

87 - 80 = 7db. 10*log_10(7) ~ 5.

mgb_phys