Phase Difference: Solving Homework Problems

[crazyog]

Homework Statement

Two sinusoidal waves in a string are defined by functions
y1= (2.00cm)sin(20x-32t)
y2=(2.00cm)sin(25x-40t)
where y and x are cm and t is sec
(a) What is the phase difference between these two waves at the point x = 5 cm and t = 2 s?
(b) What is the position x value closes to the orgin for which the two phases differ by +/- pi at t = 2 s? (This location is where the two waves add to zero)

Homework Equations

I use the equation given to me as y1 and y2
not sure if there is an equation for phase difference

The Attempt at a Solution

(a) I plugged in 5 cm and 2 s for y1 and y2
y1 = -1.9835 and y2 = 1.7018
but I am not sure what these answers mean and if they are relevant
b) (2sin(20x-32*2) + 2sin(25x-40*2) = 0 and solve for x? Is this correct?Do I do inverse sin and then move the (32*2 and 40*2) to the other side?

Thanks for any help!

 

[kreil]

A few words on phase difference:

Phase is a way of telling "where" the graph of a function is.

For example, the graph of sin(x) is 0 at x=0 and 1 at x=pi/2. If I were to change the function to sin(x-pi/2), then the function would be -1 at x=0 and 0 at x=pi/2.

Effectively, I dragged the entire graph of the function to the right by pi/2, so we would say that this second function has a phase of pi/2 relative to the first (phase is typically only important when comparing two functions).