Change in Decibals of a Pig Pen?

bdh1613

1. The problem statement, all variables and given/known data

The noise level coming from a pig pen with 176 pigs is 73 dB. Assuming each of the remaining pigs squeal at their original level after 69 of their companions have been removed, what is the decibel level of the remaining pigs?
Answer in units of dB.

2. Relevant equations

I= P/A
B=10dbLog(Is/Io)


3. The attempt at a solution

I was thinking that the ratio of the intensities would be equal to the change in the number of pigs.

73dB - x = 10Log(69)

I found that x= 54.61150909db.
However this was wrong.
I did a similar problem to this regarding people were a single person can speak at 65dB. The question asked how many people does it take to reach 78dB. In that particular problem the ratio was equal to the number of people. I think this was the case because we had a base value for what a single person could produce. In the problem with the pigs there isn't necessarily a based value for dB. Where am I going wrong in my approach? I spelled decibels wrong in the title, my bad.

bdh1613

SOLVED

I realized what I was doing wrong. The logarithmic is defining two intensities that are comparing values. The reason that the comparison was equal to the number of people was because that it was 20people to 1 person. In the case of the pigs the comparison is not equal to 69, rather it is equal to 176/107.This is how it looks

73 -x = 10Log(176/107)

x=70.8387111dB