Value of a wave at a time with a phase shift.

[Jake 7174]

Homework Statement

Calculate the value of the wave at t = (2, 3, 4, 10) ns

0.4 cos(10^8 * t + (1/3) * y) az

Homework Equations

N/A

The Attempt at a Solution

This is the last part of a problem. I have already found the phase shift of 1/3 and wavelength of 6 pi.

I have already been given the solution to time = 10 ns it is -0.1665

The professor noted at time 10 ms y=1. This was not given in the problem. He only put it in the solution How the heck did he find this? I realize that the second term in the equation corresponds to a phase shift but If it is in terms of a variable how do I know what it is at time = anything?

Can someone help me figure out how to do this. I can take it from there. This is not for graded homework. I am studying for the final on Monday.

 

[haruspex]

I do not understand what the y represents. A phase shift is usually just an additive constant, like φ in A cos(ωt+φ). If this is a traveling wave in the X dimension then I would expect A cos(ωt-x/λ+φ), or somesuch, but in that case you would need to specify both t and x to find the value. Can you provide more context for the equation?