How Do You Calculate Transverse Wave Speed from a Wave Function?

[newton10.3]

I'm trying to calculate transverse wave speed for a point on a taut string when the y displacement is 12.0 cm. The given wave function is 15.0 cm cos(Pi*x-15Pi*t), and that is all I am given. How do you do this?

 

[JaWiB]

Are you sure you're looking for the wave speed? It seems like the speed of the wave shouldn't depend on position in the string. Maybe you're looking for the speed of a point on the string?

 

[newton10.3]

That could be. The question states "What is the transverse speed for a point on a taut string" with the parameters I stated before.

 

[mezarashi]

Since wave speed doesn't depend on the x-position, you can zero it and remove it from the equation, then you are left with a simple: y= f(t) relationship.

Recalling some calculus and allowing me to rephrase the question should do the trick. What is the rate of change dy/dt when y is 12.