Finding phase difference based on distance

[Eigengrau]

Homework Statement

A tuning fork is in a hall 47.0 m long, and is placed 14.0 m from one end. It generates a tone of 246Hz. What is the phase difference when the waves traveling in each direction bounce back and meet each other?

Homework Equations

Calculated wavelength with 343/246. Also tried 2pi*38m/1.39m = phi. Also maybe (cos phi/2)sin(kx-omega*t+phi/2)

The Attempt at a Solution

Well, I figured that I could make it simple, calculate the wavelength, divide the difference in distance traveled by wavelengths, getting 27.4 waves, and then multiply .4 * 360 to get things into degrees. This gives me 144 degrees, but the answer in the back of the book is 91.3 degrees. What am I doing wrong?

Thanks in advance.

 

[Eigengrau]

Had a chance to talk to the prof, and it turns out my method was correct, but my sig figs were off. Apparently, to get a correct answer, it was necessary to assume the distances were correct to about 5 sig figs, even though the book conventionally requires only 3 and the givens were all in 3 sig figs. Poorly written question IMO.