A transverse sinusodial wave on a string has a period of T=25.0ms and travels in

Question

A transverse sinusodial wave on a string has a period of T=25.0ms and travels in the positive x direction with a speed of 20.0 m/s. At t=0, an element of the string at x=0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s.

I calculated some of the values below:

The wavelength = .75m

The Period = .025m

The speed of propagation = 30.0 m/s

The amplitude = .022 m

The initial phase angle of the wave =1.19 rad

I need the following problems worked out:

Write the wave function for the wave. Prove that the wave function satisfies the wave equation.

What is the maximum transverse speed of an element of the string?

Please show the problem worked out step by step!

Give any explanations that would help me understand. Thanks!

Explanation / Answer

Period = .025m so w= 2*pi/T =251 rad/s

k= 2 pi/ wavelength = 8.377

so y= 0.022 sin ( 251 t - 8.377 x +1.19)

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