Phase Difference of Wave and Reflected Wave

[lordy2010]

Homework Statement

A source is transmitting a sound wave of frequency 115 Hz. A receiver detects the direct sound wave and the sound reflected from a small section of wall. Speed of sound is 345 m/s.

It also gives a diagram of sound waves leaving a source, one hitting the wall, reflecting, and traveling a total of 26 metres to reach the receiver and the other going 24 metres directly to the receiver.

What is the phase difference between the direct and reflected wave?

Homework Equations

$$\lambda = \frac{v}{f}$$

$$\Delta\phi = 2\pi\frac{d}{\lambda}$$

The Attempt at a Solution

I thought the phase difference was just kd, where k = 2pi / wavelength. So I went and figured out d which is 26 - 24 = 2, and wavelength, which turned out to be 3 m.
I got as my answer 4.189 radians (240 degrees).
Then, when I looked at the solution for the problem, they had done the same thing as me, but they put +- pi at the end... So they got 4.189 +- pi = 1.047 radians (60 degrees).
But even after looking at the soluton, I have no idea why they put the +- pi at the end...

 

[ehild]

There is pi phase change when the wave reflects from the wall. The wall is a "fixed end".

ehild

 

[lordy2010]

Thanks a lot! I completely forgot about that