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Simple wave properties

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Two Velocities in a Traveling Wave
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
.
Part A
Find the velocity of propagation of this wave.
Express the velocity of propagation in terms of some or all of the variables , , and .
= ______________

Part B
Find the y velocity of a point on the string as a function of and .
Express the y velocity in terms of , , , , and .
= ____________________

Part C
Which of the following statements about , the x component of the velocity of the string, is true?

has the same mathematical form as but is out of phase.

Part D
Find the slope of the string as a function of position and time .
Express your answer in terms of , , , , and .
= ___________________
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