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Properties of waves

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For each of the following wave functions:

Ψ1 = cos [π (3 x - 4 t)]
Ψ2 = Ψ0 sin [ 0.3x + 0.6 π t]

Determine the value and give units of frequency, angular frequency, wavelength, period, and amplitude. Assume x in expressed in meters and t in seconds.

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Write the wavefunctions in the following standard form:

Psi = Psi_0 Sin(k x - omega t + phi)

or

Psi = Psi_0 Sin(k x + omega t + phi)

The first expression represents a wave moving in the positive x direction, while the second form ...

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A detailed solution is given. The properties of waves are discussed.

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Two Velocities in a Traveling Wave

(See attached file for full problem description with proper equations)

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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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