00:01
For question one, we'd like to consider the first eight harmonics of string b.
00:05
For which of these eight harmonics does a frequency match the following? okay.
00:13
So our nth frequency of a is given by this expression.
00:17
Fn is equal to va times n divided by 2 times l .a.
00:23
Here, l .a is just equal to l .a.
00:26
Is equal to our square root of t divided by mu, our linear mass density.
00:33
So f, n a is equal to n divided by 2l times a square root of t divided by mu.
00:40
T and mu are given as constant.
00:44
Similarly, for b, now lb is equal to 4l.
00:49
So f of nb is equal to n divided by 8l times our square root of t divided by mu.
00:57
So for a, we can use our values to find f of 1a equal to 1 over 2l times our square root of t divided by mu, f of 2b is equal to 4 divided by 8l times a square root of t over mu, which is just 1 half l times a square root of t over mu.
01:20
So b's fourth harmonic is equal to a's first harmonic.
01:28
For question b, similarly, b's eighth harmonic is equal to a's second harmonic...