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Tranverse velocity of a point on a string

  • Thread starter jegues
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  • #1
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Homework Statement



A sinusoidal wave is moving along a string. The equation governing the displacement as a function of position and time is,

[tex]y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],[/tex]

where x and y are in meters, and t is in seconds. At t = 2.4s, what is the transverse velocity of a point on the string at x = 5.0m?

Homework Equations





The Attempt at a Solution



I don't know how to get started on this one.
 

Answers and Replies

  • #2
collinsmark
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I don't know how to get started on this one.
"Transverse" means perpendicular to the string. The "transverse velocity" is not the speed of the wave. Rather it is the velocity of a tiny point on the string itself (attached to the string).

You are given the displacement of that point on a string, using the given equation,

[tex]
y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],
[/tex]

What's the relationship between displacement and velocity (in terms of integrals, derivatives, etc.)?
 
  • #3
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2
"Transverse" means perpendicular to the string. The "transverse velocity" is not the speed of the wave. Rather it is the velocity of a tiny point on the string itself (attached to the string).

You are given the displacement of that point on a string, using the given equation,

[tex]
y(x,t) = 0.12sin[8 \pi(t-\frac{x}{50})],
[/tex]

What's the relationship between displacement and velocity (in terms of integrals, derivatives, etc.)?
Velocity is just [tex]\frac{dx}{dt}[/tex] isn't it?
 
  • #4
collinsmark
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Velocity is just [tex]\frac{dx}{dt}[/tex] isn't it?
dx/dt is the change in position per unit time (i.e. velocity) of something along the length of the string, assuming the string lies along the x-axis.

But a point on the string itself does not move along length of the string. It moves in a perpendicular, transverse direction. Specifically, it moves in the y direction. :wink: You're looking for dy/dt.
 
  • #5
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dx/dt is the change in position per unit time (i.e. velocity) of something along the length of the string, assuming the string lies along the x-axis.

But a point on the string itself does not move along length of the string. It moves in a perpendicular, transverse direction. Specifically, it moves in the y direction. :wink: You're looking for dy/dt.
Okay so,

[tex]\frac{dy}{dt} = 0.12 \cdot 8\pi cos(8 \pi t - \frac{8 \pi x}{50})[/tex]

When I plug the numbers in I get,

[tex]\frac{dy}{dt} = 1.6m/s[/tex]

Which is still incorrect?
 
  • #6
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Bump, still looking for help on finishing this one off!
 
  • #7
ehild
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Check the evaluation, if you did not mix radians with degrees.

ehild
 
  • #8
SammyS
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Bump, still looking for help on finishing this one off!
I got 2.868 m/s.
 

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