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Transverse Speed of a particle on a wave

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


The equation of a transverse wave traveling along a very long string is given by y = 6.0sin(0.012pi*x + 4.9pi*t), where x and y are expressed in centimeters and t is in seconds.

Find the maximum transverse speed of a particle in the string.


Homework Equations





The Attempt at a Solution


I want the speed, or rate of change of position, or derivative of position. The given equation represents the transverse displacement, so, at t = 0, I would have y' = 6*0.012picos(0.012pi*x). Since y(x, t) is a sine function, the greatest slope would be at (0, 0), so y'(0, 0) would represent the greatest rate of change of y(x, t).

So the maximum transverse speed of a particle in the string would be 6*0.012*pi, correct?

This, however, is not the right answer, so why not?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
5
You have to take the derivative with respect to time.
 
  • #3
3,732
414
The speed is the time derivative.
 

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