Calculating Amplitude of Transverse Wave

[howsockgothap]

Homework Statement

The wavefunction of a transverse sinusoidal wave on a string has the form y(x,t) = Acos(kx + ωt + φ), where x and y are in m, t is in seconds and φ is the phase constant in radians. The wave has a period T = 24.5 ms and travels in the negative x direction with a speed of 31.4 m/s. At t = 0, a particle on the string at x = 0 has a displacement of 2.05 cm and travels downward with a speed of 2.15 m/s. What is the amplitude of the wave?

Homework Equations

y(x,t) = Acos(kx + ωt + φ)

The Attempt at a Solution

I am genuinely up **** creek without a paddle on this one. I have no idea how to go about it. I thought it was as simple as filling in the variables but then realized that I don't have the phase constant and I don't want to assume there is none because the next part of the question asks for the phase constant. At this point all I really need is a gentle nudge in the right direction I think.

 

[Hypersphere]

Well, you have two conditions at the origin, don't you? Try using both of them.