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

AI Thread Summary
To calculate the transverse wave speed from the given wave function, focus on the relationship between displacement and time. The wave function provided is 15.0 cm cos(πx - 15πt), indicating that the wave speed is constant and does not depend on position. To find the transverse speed at a specific displacement of 12.0 cm, differentiate the wave function with respect to time, yielding the rate of change dy/dt. This approach simplifies the problem by eliminating the x-variable, allowing for a direct calculation of the transverse speed at the specified displacement. Understanding this relationship is key to solving the problem accurately.
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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?
 
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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?
 
That could be. The question states "What is the transverse speed for a point on a taut string" with the parameters I stated before.
 
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.
 
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