# Determining phase shift of two frequencies

1. Oct 6, 2016

### teetar

1. The problem statement, all variables and given/known data
I'm given two frequencies: 4,000 Hz, and 5,000 Hz.
They are completely in-shift at time $t=0$.
I am to find the time it takes them to get completely out of phase.
2. Relevant equations

3. The attempt at a solution
I've not gotten waves very well thus far in physics. My teacher said being completely out of phase occurs at a phase shift of one half wavelength, or, at π rads. Where do I start?

2. Oct 6, 2016

You need to write each wave as $E(t)=A \, cos(2 \pi f t)$ where $f$ is the frequency, because $f=1/T$ where $T$ is the period (time of one cycle). The number * inside the cos(*) will define the phase of the wave at time t. I've probably already given you more information than we are supposed to, but hopefully you can work it from here.

3. Oct 6, 2016

### teetar

So, is it as simple as saying that the waves are completely out of shift when 10,000πt - 8,000πt = π, meaning that t = 1/2,000? I must be oversimplifying this without fully understanding the fundamental ideas behind it. Am I evaluating the change in the cosine equal to π rads (cos(10,000πt) - cos(8,000πt) = π)? Or am I still missing the obvious answer?

4. Oct 6, 2016

You did it correctly and the answer is in seconds (t=.0005 seconds).

5. Oct 6, 2016

### teetar

Thanks for the help! I definitely need to spend more time studying waves.

If anyone passes by this thread and knows of any good resources, could you reply to me with them, or PM me them? I looked all over Google trying to answer this question and didn't find many relevant sources.

6. Oct 11, 2016

### rude man

Phase is the total argument of sin or cos which evolves over time.
So if you have x1 = sin(2πf1t) and x2 = sin(2πf2t) then the phases are 2πf1t and 2πf2t and the equation to solve is 2πf1t = 2πf2t + π with f1 > f2.
There are an infinite number of answers but you want to find the shortest time t satisfying the equation.