# Phase difference of two reflected wave

Suppose a tuning fork generates sound waves with a frequency of 100 Hz. The waves travel in opposite directions along a hallway, are reflected by end walls, and return. The hallway is 47.0 m long and the tuning fork is located 14.0 m from one end. What is the phase difference between the two reflected wave at the point of the tuning fork.

My attempt:

For this question, I was able to solve using the path length difference. However I tried to solve it using wave equation,

i.e. $$y_1 = A \cos(kx - wt),\ y_2 = A \cos(kx + wt)$$

The two waves travel in opposite directions, so $$w$$ has different signs. I was planning to compute the $$kx-w$$t term for $$y_1$$ and $$y_2$$, then the phase difference will be the difference of those two phases, but I was unable to get the right answer. I think the reflection shift the phases of $$y_1$$ and $$y_2$$ by $$\pi$$, so the effect of reflection can be omitted.

Can anyone please explain what $$x$$ and $$t$$ should be when the two reflected waves meet at the point of tuning fork?