00:01
Our wave function y is given as 0 .12 times sine of pi over 8 plus 4 pi t.
00:09
So pi over 8 is k and omega our angular speed is omega.
00:16
The amplitude of the wave is 0 .12 meters.
00:21
So first let's calculate our transverse speed.
00:25
Our transverse speed will call it b y is simply dy by d y.
00:33
And that's equal to by taking the time derivative of the above expression 0 .12 meters times 4 pi times the cost times 4 pi times the cost of pi 5 8 over x plus 4 pi so if we were to calculate the transverse speed at a time of 0 .2 seconds and a displacement of 1 .6 meters, substitute that into expression above, we would get the transverse speed at this point to be minus 1 .51 meters per second.
01:38
So to calculate, next, the transverse acceleration, this is simply the derivative with respect to time of the transverse acceleration.
01:49
And from the expression above we get another expression by differentiating it once more with respect to t.
01:58
Then we get 0 .12 times 4 pi all squared, multiply by sine pi over 8 times x plus 4 pi pi t.
02:17
For the same instant of time 0 .2 seconds and distance 0 .6 meters, if we substitute these values into the expression, we get that the acceleration at this point is zero.
02:46
Next, we wish to calculate the wavelength of this wave...