Phase difference between points on wall

In summary, the question asks what the difference in phases is between two points 5 m apart along a sea wall when parallel water waves with a wavelength of 10 m strike the wall at an angle of 30°. Using the equation Δφ = Δx / λ, we can determine that the phase difference is 90°, as the wave needs to advance 2.5 m (5 sin 30°) in order to reach the second point.
  • #1
songoku
2,294
325

Homework Statement


Parallel water waves of wavelength 10 m strike a straight sea wall. The wavefronts make an angle 30o with the wall. What is the difference in phases between the waves at two points 5 m apart along the wall?
a. 30o
b. 45o
c. 90o
d. 156o
e. 180o

Homework Equations


Δφ = Δx / λ

The Attempt at a Solution


I don't think I can just put Δx = 5 m and calculate using the formula but I have no idea how to start. How can the angle given being used to find the phase difference?

Thanks
 
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  • #2
songoku said:
How can the angle given being used to find the phase difference?
Draw a diagram of a wavefront striking a point on the wall. Now look at a point 5m further along the wall, which the wavefront hasn't reached yet. How far will the wave need to advance to reach that point?
 
  • #3
Let me try:
the wave needs to advance for 2.5 m (5 sin 30o) so the phase difference = 2.5 / 10 rad = 90o

Is that correct? Thanks
 
  • #4
songoku said:
Let me try:
the wave needs to advance for 2.5 m (5 sin 30o) so the phase difference = 2.5 / 10 rad = 90o

Is that correct? Thanks
90° is correct, but you mean 2.5/10 (2π) radians.
 
  • #5
haruspex said:
90° is correct, but you mean 2.5/10 (2π) radians.
Yes, my bad

Thank you very much haruspex
 

1. What is the phase difference between points on a wall?

The phase difference between points on a wall refers to the difference in the timing of the oscillation of sound waves at different points on the wall. It is measured in degrees or radians and is a result of the sound waves traveling different distances to reach each point.

2. Why is phase difference important in acoustics?

Phase difference is important in acoustics because it affects the quality of sound that is perceived. When sound waves are in phase (i.e. their peaks and troughs occur at the same time), they reinforce each other and produce a louder and clearer sound. On the other hand, when sound waves are out of phase, they can cancel each other out and result in a weaker or distorted sound.

3. How does the distance between points on a wall affect the phase difference?

The distance between points on a wall is a determining factor in the phase difference. The greater the distance between two points, the larger the phase difference will be. This is because sound waves travel at a constant speed, so the longer distance will result in a longer time for the wave to reach the second point, causing a greater delay and thus a larger phase difference.

4. Can phase difference be measured?

Yes, phase difference can be measured using specialized equipment such as an oscilloscope or a phase meter. These devices can measure the time difference between two points on a wall and calculate the corresponding phase difference in degrees or radians.

5. How does the phase difference between points on a wall affect sound quality in a room?

The phase difference between points on a wall can have a significant impact on sound quality in a room. In a well-designed acoustical space, the sound waves should arrive at different points on the wall in phase, resulting in a clear and uniform sound. However, if there are significant phase differences between points, it can lead to unwanted reflections, echoes, and a decrease in sound quality.

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