00:02
In the given problem, the equation of the means progressive wave is given as yxt.
00:09
It means transverse displacement of the particles on y axis while the wave is traveling on the x axis.
00:21
It is equal to 9 .61 sine 4 .355 pi t is plus 0 .037 pi x.
00:49
If we compare this with the equation of the wave traveling on negative x -axis, the standard equation of the wave traveling on negative x -axis is equal to a sine omega t, say, plus kx.
01:15
Now if we compare these two equations, we will get the answers as follows.
01:24
First is amplitude.
01:25
Amplitude we can see we can compare the amplitude a equal to 9 .61.
01:32
And here x and y are given in centimeters.
01:37
So amplitude will be 9 .61 centimeter.
01:44
Now in part b, wavelength, the wavelength.
01:52
Lambda is equal to 2 pi by k where k is the propagation constant or the wave number now we can compare that k equal to 0 .037 pi so let lambda will be 2 pi upon 0 .037 pi it comes out to be 54 .05 centimeter and in part three asking about the frequency now frequency is equal to we know omega upon two pi now if we see compare the standard equations then omega is equal to 4 .35 pi omega is equal to 4 .35 pi omega is equal to 4 .35 pi is equal to 4 .35 pi is equal to 4 .35 pi is equal to 4 .35 pi divided by 2 pi it comes out to be 2 .15 hertz now in part d they are asking about speed this is the speed of the wave on the x direction now speed v is equal to omega upon k so omega b know it is 4 .355 and k is 0 .037 pi.
03:44
If we compare, it's 117 .56 centimeter per second.
03:57
Now in e, the direction of propagation is on the negative x -axis because this wave resembles with this equation resembles with the equation of the wave traveling on the negative x -axis.
04:12
This is the equation of the wave traveling on negative x -axis.
04:18
And the given equation matches in the form with the wave on the negative x -axis...