# Phase constant of waves

**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!

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