Decibel questions, how many people are cheering

[VTC-nerds]

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?

Homework Equations

Not a clue.

The Attempt at a Solution

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

 

[genneth]

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

 

[VTC-nerds]

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]

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)

 

[VTC-nerds]

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?

 

[genneth]

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

 

[mgb_phys]

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

Not quite
87-80 = 7db and I/Io = 10^(7/10) ~ 5 and Io = 1 so I = 5

 

[VTC-nerds]

Thank you.