# Phase difference past paper question

#1
Hi,
I was doing an AQA physics past paper (linked below) about phase differences.
For question 6 a ii:
I got 3/4 pi and 7/4 pi
However, the mark scheme says pi and 2pi. Surely for it to be pi and 2pi point X must be at the peak of the wave, right? Or am I misunderstanding it. Thanks!

Paper: http://filestore.aqa.org.uk/subjects...2-QP-JUN12.PDF
Mark Scheme: http://filestore.aqa.org.uk/subjects...W-MS-JUN12.PDF
0
6 years ago
#2
(Original post by gigglej)
Hi,
I was doing an AQA physics past paper (linked below) about phase differences.
For question 6 a ii:
I got 3/4 pi and 7/4 pi
However, the mark scheme says pi and 2pi. Surely for it to be pi and 2pi point X must be at the peak of the wave, right? Or am I misunderstanding it. Thanks!

Paper: http://filestore.aqa.org.uk/subjects...2-QP-JUN12.PDF
Mark Scheme: http://filestore.aqa.org.uk/subjects...W-MS-JUN12.PDF
If it was a moving wave you would be correct, however it is a stationary wave so the phase difference can only ever be where n is an integer.
1
#3
(Original post by natninja)
If it was a moving wave you would be correct, however it is a stationary wave so the phase difference can only ever be where n is an integer.
Ahh, that makes a lot of sense now! Thank you!!
0
6 years ago
#4
(Original post by gigglej)
Ahh, that makes a lot of sense now! Thank you!!
It's pretty simplified but it works

A fuller version would be this:

The equation of a travelling wave is

where k is the wavevector and omega is the angular frequency. A stationary wave is made up of two identical travelling waves in opposite directions and therefore has an opposite k vector. The superposition of these two waves is given by:

since

we can write this as:

factorising out gives us:

converting back to trig functions:

This means that particles will either have an amplitude of zero or they will be exactly in phase or exactly out of phase depending on whether is positive or negative.
0
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