00:01
All right, so we have the displacement of a string as a function of, or of a wave, excuse me, as a function of x and t, and it's something like 0 .08, presumably meters times the sign of pi over 9 times x plus 5 pi times t.
00:23
And we want to know what is the transverse speed of the wave at t equals 0 .14 seconds for an element of the string located at 1 .2 meters.
00:39
So the speed of the wave, the transverse speed of the wave is just going to be, as a function of position time, is a derivative with respect to time of y.
00:49
And so it'll be something like 0 .08 meters times 5 pi.
00:57
We'll write radians per second times the cosine of pi over 9 times x plus 5 pi times t.
01:08
And so now we just got to plug in our numbers.
01:10
0 .14 seconds, 1 .2 meters into there.
01:13
So pi divided by 9 times 1 .2 plus 5 times 5 times 5 times.
01:20
0 .14.
01:21
And then we take the sign of this, or sorry, the cosine of this...