# 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.
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...

Thanks a lot! I completely forgot about that 