# Transverse Speed of a particle on a wave

1. Apr 29, 2009

### Oijl

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

2. Apr 29, 2009

### rl.bhat

You have to take the derivative with respect to time.

3. Apr 29, 2009

### nasu

The speed is the time derivative.