A what is the decibel level of a sound that is nine times as...

(a) What is the decibel level of a sound that is nine times as intense as a 86.7 dB sound? in dB ? (b) What is the decibel level of a sound that is one-seventh as intense as a 86.7 dB sound? in dB ?

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Transcript

0:00 Hello.

00:02 So here we're talking about decibel sounds.

00:05 So the general formula is given by b equals 10 log i over i not that is the original intensity.

00:24 So for the first part we have 86 .7 10 log i of i over i not.

00:50 Let's just say something like b prime.

00:55 It's going to be which is all we're trying to find, right? because 10 love i.

01:08 Prime over i .0.

01:09 So the i .0 doesn't change.

01:14 So let's say this is first equations, second equation.

01:20 We can subtract these two equations.

01:23 Can we do some subtraction? so let's see.

01:26 So if you do, we can have 86 .7 minus y equals 10 lads high over i not minus 10 lube prime over i not okay so let's find a beta or beta one that's going to be equal to so if you isolate that we're going to have 86 .7 minus just be careful here yeah this is a plus 10 love i 1 over i not minus 10 love i over i not so let's see level 1 so initially these two values i and i not are the same so we're going to cancel out.

03:26 And so log 1 is 0.

03:29 So this side goes over to 0.

03:31 So beta 1 is going to be 86 .7 plus.

03:37 What did i do here? this is 10 loaves.

03:48 Love i prime over i now.

03:54 So remember that initially, i if it was i 9.

03:59 So this cancels you have lov 1, log 1 is 0...