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Wave Motion, writing an equation.

  • Thread starter Ithryndil
  • Start date
  • #1
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Homework Statement



A sinusoidal wave traveling in the -x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 29.0 cm, and a frequency of 15.0 Hz. The transverse position of an element of the medium at t = 0, x = 0 is y = -3.00 cm, and the element has a positive velocity here.

Write an expression for the wave function y(x,t), where y and x are expressed in cm, and t is expressed in seconds.



Homework Equations



[tex]\omega = 2\pif[/tex]

v=(lambda)(frequency)

[tex] k = 2\pi/\lambda[/tex]

[tex] y(x,t) = Asin[\left(2\pi/\lambda\right)(x - vt)][/tex]

The Attempt at a Solution


We are given the fact that:

[tex]A = 20.0cm[/tex]

[tex]\lambda = 29cm[/tex]

[tex] v = (lambda)(frequency) = 435cm/s[/tex]

I think the answer is the following, but I am not sure, and I only have one more submission left, so I want to be sure.

[tex] y(x,t) = -20.0cos[.217(x-435t)][/tex]
 
Last edited:

Answers and Replies

  • #2
142
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Anyone have any idea if I am correct?
 
  • #3
alphysicist
Homework Helper
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Hi Ithryndil,

If you check your answer at x=0 and t=0, you get that y=-20 cm. However, this is not what the problem specifies; they say they want x==-3cm at x=0 and t=0.

I think you need to include a phase constant in your expression that will give the correct initial condition.
 
  • #4
142
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You mean y = 3 cm? And I think so too. I just realized that the general equation for y(x,t) is as follows:

[tex]
y(x,t) = Asin(kx - vt + \phi)]
[/tex]

I think the above equation is for a wave traveling to the right. I think because this wave is traveling to the left it needs to be:

[tex]
y(x,t) = Asin(kx + vt + \phi)]
[/tex]
 
  • #5
alphysicist
Homework Helper
2,238
1
Yes, I did mean y= -3 cm. Sorry!

Your updated equation looks good. Once you plug in the numbers you found, you can check that it matches y=-3cm at x=0 and t=0 and that it also has a positive velocity (in the y direction at that point).
 
  • #6
142
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Alright, thank you for the help.
 
  • #7
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,098
129
[tex]
y(x,t) = A\sin(kx + vt + \phi)]
[/tex]
That is almost correct. There should either be some more parentheses inside the sin argument, or replace vt with [tex]\omega t[/tex].
 
  • #8
142
0
You're right, it should be: [tex]y(x,t) = A\sin(kx + \omegat + \phi)[/tex]

I wound up getting the following for the equation:

[tex]y(x,t)20.0sin(0.217x+94.25t-0.1506)[/tex]

Now I was stupid and input [tex]y(x,t)20.0cos(0.217x+94.25t-0.1506)[/tex]...note I put cosine and not sine. Yes, the cosine would be correct with the right phase angle, but it's not with that phase angle.
 
  • #9
Redbelly98
Staff Emeritus
Science Advisor
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Insights Author
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Your expression (using sin) looks good. :smile:
 
  • #10
142
0
Thank you. I just can't believe I inputted the expression with cos instead of sin.
 

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