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

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Homework Help Overview

The discussion revolves around calculating the transverse wave speed for a point on a taut string using a given wave function. The wave function provided is 15.0 cm cos(πx - 15πt), and the specific displacement at which the speed is to be calculated is 12.0 cm.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore whether the calculation pertains to wave speed or the speed of a point on the string. There is a discussion about the relationship between wave speed and position, with some suggesting a focus on the time-dependent aspect of the wave function.

Discussion Status

The conversation is ongoing, with participants questioning the interpretation of the problem and clarifying the distinction between wave speed and the speed of a point on the string. Some guidance has been offered regarding simplifying the wave function to focus on the time variable.

Contextual Notes

Participants note that the problem may involve assumptions about the wave speed being independent of position along the string, and there is a mention of needing to consider the rate of change of displacement with respect to time.

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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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