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Transverse Wave Traveling In A String: Two Wave Velocities

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Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e.g., air or a string) and the velocity of the medium (the air or the string itself).

Consider a transverse wave traveling in a string. The mathematical form of the wave is:

y(x,t) = A sin(kx-omega t).

1. Find the slope of the string frac{partial{y(x,t)}}{partial{x}} as a function of position x and time t.
Express your answer in terms of A, k, omega, x, and t.
*** =Akcos((kx-omega*t).

a) Find the ratio of the y velocity of the string to the slope of the string calculated in the previous part.
Express your answer as a suitable combination of some of the variables omega, k, and v_p.

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Solution Summary

The solution investigates the velocities of the transverse wave traveling in a string (see attached file).

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