# Homework Help: Simple wave problem - phase constant

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1. May 5, 2016

### i_hate_math

1. The problem statement, all variables and given/known data
The figure shows the displacement y versus time t of the point on a string at x = 0, as a wave passes through that point. The scale of the x axis is set by ys = 84.0 mm.The wave has form y(x, t) = ym sin (kx - ωt+φ). What is φ? (Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of ω into y(x, t) and then plotting the function.)

2. Relevant equations
y(x, t) = ym sin (kx - ωt+φ)

3. The attempt at a solution
This is supposed to be really easy but the solution I got was wrong. My approach was straight forward:
read off the initial y value --- y(0,0)=0.028
and sub in the equation: 0.028=0.084sin(0-0+φ)
The question mentioned that the calculator might give the wrong value but I do not see how I could make amend to it.

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2. May 5, 2016

### blue_leaf77

At $x=0$, you have $y = -A\sin(\omega t -\phi)$, this is the curve $y = -A\sin(\omega t)$ translated by $\phi$. When you compare $y = -A\sin(\omega t)$ with the picture you uploaded, you should see that $\phi$ should be in the second quadrant.

3. May 5, 2016

### i_hate_math

I see where I went wrong, thank you very much for the help!

4. May 5, 2016

### i_hate_math

Though, are you sure its in the second quadrant? I think it should be π+0.340 and thats third quadrant

5. May 5, 2016

### blue_leaf77

That cannot be the case because sine of an angle in 3rd quadrant is negative, on the other hand the displacement is positive in your picture.

6. May 5, 2016

### i_hate_math

So it would be π-0.34? This gives a value thats in the 2nd quad

7. May 5, 2016

Yes.