Decibel questions, how many people are cheering

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Homework Help Overview

The problem involves calculating the number of people cheering based on sound intensity levels measured in decibels. The original poster presents a scenario where each individual contributes to a sound level of 80 dB, and the total sound level is 87 dB.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the concept of decibels and the relationship between sound intensity and the number of sources contributing to the sound level. Questions arise about the need for logarithmic calculations versus simpler methods.

Discussion Status

Participants are exploring different ways to approach the problem, with some suggesting that logarithmic calculations may not be necessary. There is an ongoing examination of how to relate the increase in decibels to the number of individuals contributing to the sound.

Contextual Notes

There is a mention of the original poster's confusion regarding the use of logarithmic equations and the desire for a more straightforward method to arrive at the answer. The discussion reflects a lack of consensus on the best approach to solve the problem.

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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?
 
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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?
 
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.
 
genneth said:
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
 
Thank you.
 

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