Phase Difference: x & y, x & z - Explained

[Millie Baker]

Homework Statement

State the phase relationship between
x and y
x and z
(shown in photo)

The Attempt at a Solution

I got the phase difference between x and y to be 135 degrees and then between x and z to be 45 degrees. However the mark scheme gives the answers 180 degrees and 0 degrees. Please can someone explain why this is?

 

[gneill]

Hi Millie Baker,

Welcome to Physics Forums!

I got the phase difference between x and y to be 135 degrees and then between x and z to be 45 degrees. However the mark scheme gives the answers 180 degrees and 0 degrees. Please can someone explain why this is?

The phase relationship pertains to the relative directions of motion at the specified positions rather than the difference in angle of the sinusoid of the stationary wave. So imagine that at some instant point x is moving upwards (or downwards), what directions would you expect the motion to be for points Y and Z?

 

[Millie Baker]

Hi Millie Baker,

Welcome to Physics Forums!The phase relationship pertains to the relative directions of motion at the specified positions rather than the difference in angle of the sinusoid of the stationary wave. So imagine that at some instant point x is moving upwards (or downwards), what directions would you expect the motion to be for points Y and Z?

Ah I'm sorry I didn't make it clear which part of the question I need help with! I was asking about the second part (ii), where the question is 'state the relationship between...'

 

[gneill]

Ah I'm sorry I didn't make it clear which part of the question I need help with! I was asking about the second part (ii), where the question is 'state the relationship between...'

Yes, I understand. My comment addressed that. Two particles moving in the same direction at the same instant have a phase relationship of zero degrees (they are said to be "in phase"). If they move in opposite directions at the same instant then their phase relationship is 180 degrees (they are said to be "out of phase").

 

[Millie Baker]

Okay, I think I understand now. Thank you.

 

[CWatters]

Millie - I think you might have been confusing transverse stationary waves with traveling waves.

 

[Millie Baker]

Millie - I think you might have been confusing transverse stationary waves with traveling waves.

Ah okay, so if the wave was not reflected, would my answer be correct?

 

[CWatters]

If not reflected then the drawing would be quite different. You would need a video rather than a drawing.

Note the horizontal axis in your picture is "position on the string" not time. Had it been a graph of the displacement vs time for a single point on the string then the points x and y would have been 135 degrees apart.