00:03
So we're given the relationship between beta, which is a sound level in decibels and sound intensity, which is in watts per meter squared, and the sound intensity at the threshold of sound.
00:17
And we're also given a pair of the sound level at the threshold of pain and the intensity of that sound, again, at the threshold of pain.
00:28
That's where sound hurts.
00:29
And what we want to do is determine the sound intensity at the threshold of hearing.
00:36
So in order to do that, we're going to solve our equation for i0 or i sub 0.
00:41
That means we have to isolate the logarithm, so we divide both sides by 10, base 10 of i over i not.
00:50
And then we're going to perform the inverse operation.
00:55
We're going to exponentiate.
00:56
So we're going to start with that same base because for exponentials and logs to be inverses, they have to have the same base, so base 10.
01:03
Then what used to be the output becomes the input, so our new exponent is beta over 10, and what used to be the input becomes the output.
01:12
So this all equals i over i sub -zero.
01:17
Now we can multiply both sides by i -sub -0 and divide both sides by 10 to the beta over 10, and we get that i -subs -0 equals i, the intensity, divided by 10 to the beta over 10...