The wave function for a traveling wave on a taut string is...

The wave function for a traveling wave on a taut string is (in SI units) y(x,t) = 0.370 sin(5ðœ‹t - 2ðœ‹x + ðœ‹/4) (a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.132 m? (c) What is the wavelength of the wave? (d) What is the frequency of the wave? (e) What is the maximum transverse speed of an element of the string?

Transcript

00:01 In this given question, you are given with a wave function of traveling wave on a tot string, which is y, which function is given as 0 .370, sine 14 pi t minus 5 pi, x plus pi divided by 4.

00:35 And we have to solve five parts of this question.

00:39 So let's solve for the first one which is we have to calculate the speed and the direction of the travel of the wave.

00:47 Okay, so let's solve the first one.

00:51 The general equation, the general equation is given by yxt is equal to a sine omega t minus k x plus 5 so from here omega comes out as 14 pi k comes out as 5 pi and a comes out as when we compare these two equations 0 .370 meters so the speed v is omega divided by k which is 14 pi divided by 5 pi so from here v comes out as 2 .8 meter per second and the direction is positive x -axis positive x -axis direction this is our a part now let's solve for the b part b part in b part we have to calculate the vertical position of the element of a string at t equals to to t equals to zero second and x is equal to 0 .122 meter.

02:55 So from here, let's solve it.

02:59 Y, when we put the values of t and x 0 comma 0 point, sorry, y zero point x is 122 and 0.

03:25 So when we put the values of, so a is 370 sine omega t 0 minus 5 pi into 0.

03:45 0 .122 plus pi by 5 .2 plus pi by pi divided by 4, which is when we solve this, 0 .370 sine minus 0 .61 pi plus 0 .25 pi so from here 370 sine minus 0 .36 pi and it comes out at 0 .370 sine multiplied by 180 divided by 180 divided by 180 divided by pi so from here it comes out as minus 0 .33478 meters this is the answer of our second part b part now let's solve for the c part in c part we have to calculate the wavelength okay wavelength lambda c lambda so lambda is equal to 2 pi by divided by k 2 pi divided by k it comes out as 2 pi k is 5 pi 5 pi so from here wavelength comes out as 0 .4 4 0 .4 meters okay now the next part part d we have to calculate the frequency frequency which is omega by 2 pi omega by 2 pi.

06:26 So it comes out as 14 pi.

06:29 Omega is 14 pi divided by 2 pi.

06:33 So frequency comes out as 7 hertz...

Question

Please give Ace some feedback