# Phase Difference of Wave and Reflected Wave

• lordy2010
In summary, the problem involves a source transmitting a sound wave of frequency 115 Hz and a receiver detecting the direct sound wave and the sound reflected from a small section of wall. The speed of sound is 345 m/s. The phase difference between the direct and reflected wave can be calculated using the equations \lambda = \frac{v}{f} and \Delta\phi = 2\pi\frac{d}{\lambda}. The solution involves taking into account the pi phase change when the wave reflects from the wall, resulting in a phase difference of 4.189 +- pi = 1.047 radians (60 degrees).

## 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...

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

ehild

Thanks a lot! I completely forgot about that

## 1. What is the phase difference between a wave and its reflected wave?

The phase difference between a wave and its reflected wave is the difference in phase, or the position of a point on the wave, between the two waves. This can be seen as the difference in the height or position of a wave peak or trough between the original wave and the reflected wave.

## 2. How does the phase difference affect the resulting interference pattern?

The phase difference between a wave and its reflected wave can greatly affect the resulting interference pattern. If the two waves are in phase, meaning their peaks and troughs align, constructive interference occurs and the resulting wave will have a larger amplitude. If the two waves are out of phase, destructive interference occurs and the resulting wave will have a smaller amplitude.

## 3. Can the phase difference be manipulated or controlled?

Yes, the phase difference between a wave and its reflected wave can be manipulated or controlled. This can be done through various techniques such as adjusting the angle of reflection, changing the medium through which the wave travels, or introducing a phase shift between the two waves.

## 4. How does the phase difference vary for different types of waves?

The phase difference between a wave and its reflected wave can vary depending on the type of wave. For example, sound waves and light waves have different wavelengths and frequencies, which can result in different phase differences between the original wave and the reflected wave.

## 5. What are the practical applications of understanding phase difference of a wave and its reflected wave?

Understanding the phase difference of a wave and its reflected wave is crucial in various fields such as optics, acoustics, and communications. It allows us to manipulate and control the interference patterns of waves, which is essential in technologies such as radar, sonar, and fiber optics. It also helps in understanding the behavior of waves in different mediums and can aid in the design and improvement of various devices and systems.