Traveling Waves Homework: Transverse Sinusoidal Wave

[dwong]

Homework Statement

A transverse sinusoidal wave on a string has a period T = 31.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on 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.

Homework Equations

y=Asin(kx-wt+phi)
w=2pi/T
v=w/k
v=lamdbaf

The Attempt at a Solution

Firstly, I changed the period to T=.031sec.
Solved for Omega = 2pi/(.031) = 202.6834 rad/sec
Solved for lamdba = v/f = .9299
Solved for k = 6.756

To find phi, I differentiated the y equation for v(y), then got the equation
v/v(y) = tan(phi)/-w
I got phi = 1.1125, but it is not correct. Please help. Thank you

 

[dwong]

Can anyone give me insight as to why my question is not being answered? Did I post in the wrong forum, not give enough information? Thank you all.

 

[ehild]

No, but you did not tell what was the question. phi=1.1125 radian looks correct. The amplitude was not asked?

ehild

 

[dwong]

Ah, sorry my mistake.

(a) What is the amplitude of the wave?
(b) What is the phase constant?
(c) What is the maximum transverse speed of the string?
(d) Write the wave function for the wave.

The amplitude is asked for, but I figured that I would find the amplitude after finding the phase constant.

Apparently, 1.1125 is incorrect, but if I did it correctly and it is just an error, then that's okay.
Thank you for confirming my answer.

Is there any other way of finding the phase constant? Or a way to find the amplitude without finding the phase constant first?

 

[ehild]

You have two equations :

A*sin(phi)=0.02
A*cos(phi)=2.00/w

Take the square of both equations and add them: You get A^2.

ehild