Calculating phase difference Watch

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Zwitter Ion

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Report Thread starter 11 years ago

How would you work out phase difference between two points given the frequency, distance and wavelength...and how would you express this in radians.
EG:
Wavelength of a wave is 1.2m, Speed is 3.6ms-1,distance between two points P and Q is 0.4m
What is the phase difference....
The mark scheme says 2(pi)/3.....how did they get that?? :confused:

Any help will be appreciated
Thanks in advance

ukstudent2011

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(Original post by Zwitter Ion)
How would you work out phase difference between two points given the frequency, distance and wavelength...and how would you express this in radians.
EG:
Wavelength of a wave is 1.2m, Speed is 3.6ms-1,distance between two points P and Q is 0.4m
What is the phase difference....
The mark scheme says 2(pi)/3.....how did they get that?? :confused:

Any help will be appreciated
Thanks in advance

Well assuming that the distance between them is in the direction that the wave is traveling (so one is behind the other basically), you can just work out how what how far behind they are in terms of the wavelength. So if it is 0.4m behind and has a wavelength of 1.2m it is 0.4/1.2 = 1/3 of a wavelength behind. A wave has 2pi radians, so it is 1/3*2pi = 2pi/3 out of sync.

gorilla_baby

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phase difference = 2pi x path difference divided by lambda
path difference is like (n + 1/2)lambda etc..

gorilla_baby

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so path difference = 1/3 lambda and thus the two lambda's in the equation cancel out leaving phase difference = 2pi x (1/3) = 2pi/3
that gives you the answer

Zwitter Ion

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So am i right in saying that a general formula to calculate phase difference is:

distance travelled/wavelength x 2(pi) ???

gorilla_baby

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not distance travelled, but the difference in the distance between the two points in terms on lambda, i.e.a multiple or fraction of the wavelength

dannyphantom

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Use the formula,
=2 pi d / wavelength
Put the values,
=2(pi)(0.4)/1.2
=2pi/3

Amirtha

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i came across a question with the same information:1. they've given a displacement/distance graph with a straight line running through the x axis saying its a stationary wave at t=0.
2. then they say it has a period of 20ms and wavelength 1.2m. max amplitude is 5mm
they ask what is the phase diff between particles of the string at .4m and .8m.
the MS says 180 degrees/ pi radians

can someone explain this to me?

astro67

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(Original post by Amirtha)
i came across a question with the same information:1. they've given a displacement/distance graph with a straight line running through the x axis saying its a stationary wave at t=0.
2. then they say it has a period of 20ms and wavelength 1.2m. max amplitude is 5mm
they ask what is the phase diff between particles of the string at .4m and .8m.
the MS says 180 degrees/ pi radians

can someone explain this to me?

Not sure entirely about the nature of the question - straight line displacement as a function of distance doesn't look like a wave but assuming the statement that we're looking at a stationary wave applies, we can draw certain conclusions. A stationary wave with a node at x = 0 and wavelength 1.2m will have nodes at x = 0.6 m, 1.2 m, 1.8 m etc. Points either side of a node will oscillate out of phase with each other, so the phase difference between them will be pi radians or 180 degree. This is true for any points either side of a node. Points at x = 0.4m and x = 0.8m are equal distances from the 0.6 m node so they will oscillate out of phase with each other with equal amplitude to each other.

Amirtha

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(Original post by astro67)
Not sure entirely about the nature of the question - straight line displacement as a function of distance doesn't look like a wave but assuming the statement that we're looking at a stationary wave applies, we can draw certain conclusions. A stationary wave with a node at x = 0 and wavelength 1.2m will have nodes at x = 0.6 m, 1.2 m, 1.8 m etc. Points either side of a node will oscillate out of phase with each other, so the phase difference between them will be pi radians or 180 degree. This is true for any points either side of a node. Points at x = 0.4m and x = 0.8m are equal distances from the 0.6 m node so they will oscillate out of phase with each other with equal amplitude to each other.

i thought points either side of a node oscillate in phase. how is it not in phase?
and what if the points are not of equal distance from the node, what will be the phase difference? like between .5m and .8m?

astro67

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#11

(Original post by Amirtha)
i thought points either side of a node oscillate in phase. how is it not in phase?
and what if the points are not of equal distance from the node, what will be the phase difference? like between .5m and .8m?

This would be much easier to describe with a pictures but here goes... Points either side of a node travel in opposite directions - while one goes up, the other goes down. As a result, the string has a smooth shape therough the node itself at all times. If the string moved up and down simultaneously on both sides of a node then the string or whatever it is would have a kink at the node most of the time which would violate continuity requirements.

The motion of a point at distance x along a stationary wave can be described by A*sin(2*pi*x/lambda)*sin(omega*t). For a given value of x (i.e. a fixed point on the string), the motion is sinusoidal with time, with amplitude given by A*sin(2*pi*x/lambda). All the points between consecutive nodes are moving in phase with each other. For 0<x<(lambda/2), the amplitude is positive. For x = (any integer)*(lambda/2), then the amplitude is zero and we have a node. For (lambda/2)<x<lambda, the amplitude is negative and the string travels in the opposite direction, corresponding to a phase shift of pi relative to points on the string either side of the nodes.

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