# Phase constant of waves

1. Mar 6, 2014

### grassstrip1

1. The problem statement, all variables and given/known data
I've attached the question where the graph can be found.
Essentially I have no problem determining A=0.04M K= 10π rad/m λ=0.2M ω=π/5 rad/s
I'm having trouble choosing what ø should be.

2. Relevant equations
y(x,t)= 0.04sin(10πx - π/5t +ø)

3. The attempt at a solution
Since the graph is for the particle at x=0 and t=0 and y=0
0=0.04sin(ø) solving for ø gives π, -π and 0

To try and determine the right phase constant I took the partial derivative to find the transverse velocity.
v(x,t)= (0.04)(-π/5)cos(10πx - π/5t +ø)
Since the particle has a positive velocity at t=1 , plugging in t=1 should give a positive velocity
Therefore ø cant = 0 since using 0 as a phase constant gives a negative velocity for t=1 and x=0
Problem is both plus and minus pi give the right velocity and I'm not sure how to pick the correct one. The correct answer is +π
I'd like to know in general as well how to pick the correct value. Thanks!
http://imageshack.com/a/img547/3680/2tjw.png [Broken]

Last edited by a moderator: May 6, 2017
2. Mar 6, 2014

### BvU

You did it just right. Many (me too) intuitively fill in $\phi$=0. But if you draw a sin(x), and pull it to the right, you see x=0 is moving down.

3. Mar 6, 2014

### grassstrip1

Okay thank you! I'm just wondering how you can tell the answer is positive pi and not negative since both would give the same sign for velocity

4. Mar 6, 2014

### nasu

It does not make any difference if you pick ∏ or -∏.
cos(a+∏)=cos(a-∏)=-cos(a)