Analyzing Standing Wave Phase at Points P, Q, R, S, T & U

In summary, the conversation discusses a question about a standing wave on a stretched string. The question asks for the points where the oscillation will be in phase and out of phase with the oscillation at P. The points where the oscillation is in phase are Q, R, S, and U, while the point where it is out of phase is T. The conversation also includes some discussion about calculating phase and the behavior of particles in standing waves.
  • #1
Gunman
25
0

Homework Statement


A standing wave is set up on a stretched string as shown.
At which points will the osciallation be exactly in phase witht that at P?
At which points will the oscillation be exactly out of phase with that at P?
The points are on the horizontal line.
Q at 2
P at 5
R at 8
S at 12
T at 20
U at 22



Homework Equations





The Attempt at a Solution


Well, I am unsure on how to go about doing this quesiton. How do i calculate phase for this? Sorry if I'm sounding like I didn't not attempt. But I can't seem to understand how to calculate the phase difference here?
And also the particles would vibrate perpendicular up and down right? And how come its said that the for standing waves, within 2 adjacent N all particles have the same phase?

Is it because they particles move up and down and the fraction of cycle they have completed is the same thus the graph looks the same when its going up or comming down and the graph would look otherwise(distorted) if one completes half a cycle while other has completed the whole cycle?
Is it possible to clear my doubts using this question as an example. Appreciate any help given! Thank you very much.

Hmm. Ya. I have attached the picutre. And the points are located as where I have told in the above section. Thank you again. =)
 

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  • #2
The points where the oscillation is in phase with that at P are Q, R, S, U. The points where the oscillation is out of phase with that at P are T.
 
  • #3



To analyze the standing wave phase at points P, Q, R, S, T, and U, we need to first understand what phase means in the context of waves. Phase refers to the position of a particular point on a wave relative to a reference point, usually taken as the starting point of the wave. In this case, since the standing wave is set up on a stretched string, the reference point can be taken as the point where the string is held in place.

To calculate the phase difference at different points on the standing wave, we can use the equation Φ = 2π(x/λ), where Φ is the phase difference, x is the distance from the reference point, and λ is the wavelength of the wave. In this case, since the standing wave is on a horizontal line, the distance x is simply the horizontal distance from the reference point.

At points P, R, and T, the oscillation will be exactly in phase with that at point P. This is because these points are all located at a distance of an integer multiple of half the wavelength from the reference point. In other words, they are all located at points where the wave is at the same position in its cycle.

At points Q, S, and U, the oscillation will be exactly out of phase with that at point P. This is because these points are all located at a distance of an odd multiple of quarter the wavelength from the reference point. In other words, they are all located at points where the wave is at opposite positions in its cycle.

In terms of the particles vibrating perpendicular to the string, the particles at points P, R, and T will all be vibrating in the same direction at the same time, while the particles at points Q, S, and U will be vibrating in the opposite direction at the same time. This is because at points where the oscillations are in phase, the particles are moving in the same direction at the same time, while at points where the oscillations are out of phase, the particles are moving in opposite directions at the same time.

In summary, the phase of a standing wave can be calculated using the equation Φ = 2π(x/λ), where x is the distance from the reference point and λ is the wavelength of the wave. Points that are located at integer multiples of half the wavelength from the reference point will have the same phase and points that are located at odd multiples of quarter the wavelength
 

1. What is a standing wave?

A standing wave is a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in a pattern of nodes and antinodes, where points of maximum and minimum amplitude occur, respectively.

2. What is the phase of a standing wave?

The phase of a standing wave refers to the position of a point on the wave in relation to its starting point. It is measured in degrees or radians and can range from 0 to 360 degrees, or 0 to 2π radians.

3. How is the phase of a standing wave analyzed?

The phase of a standing wave can be analyzed by measuring the displacement or amplitude at different points along the wave. This can be done using instruments such as an oscilloscope or by mathematical calculations.

4. What do the points P, Q, R, S, T, and U represent in analyzing standing wave phase?

These points represent specific locations along the standing wave where the phase is being measured. P and U are typically located at the nodes, while Q, R, S, and T are located at the antinodes.

5. Why is analyzing standing wave phase important?

Analyzing standing wave phase can provide valuable information about the properties of the wave, such as its wavelength and frequency. It can also help in understanding the behavior of the wave and how it interacts with its surroundings.

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