Finding the Equation for a Harmonic Wave at t=0

[Gogsey]

A harmonic wave traveling in the +x-direction has, at t = 0, a displacement of 17 units at x = 0, and a displacement of of -10 units at x = (3/4)$$\lambda$$. Write the equation for the wave at t = 0.

So the amplitude is the sum of the squares all square rooted of the individual values we have. Thats simple. But I'm having trouble figuring out the phase difference.

If there was no phase difference at all, then at (3/4)$$\lambda$$ the amplitude would be at its maximum displacement from y = 0, in this case approx. 20cm. However, its only 10cm from y = 0, so there must be a phase difference. But how do you calculate it.

I know the phase difference $$\phi$$ = arcsin(y/A). Now is y = 20 cm in this and the amplitude equal to 10? Not entirely sure how to use this formula, beacase I get something weird. Also not sure if I should be using this formula for this question.

 

[gabbagabbahey]

Just write down the general expression (sine/cosine with phase and amplitude), for a wave traveling in the +x-direction, and then plug in the information you are given...