Phase relation between two waves

[songoku]

Homework Statement

Please see below

Relevant Equations

$\phi=\frac{2\pi x}{\lambda}$

I answered A but the answer key is B.

I thought since the wave is moving to the right, P started first compared to Q (the crest of P is closer to y-axis compared to Q). Why is the correct answer B?

Thanks

Edit:
Wait, is it because the x-axis is position so the position of Q is in front of P (more to the right)?
If the x-axis is time, then P will lead Q since P starts earlier?

 

[DaveE]

Imagine that you are measuring the wave height at some arbitrary position on the x-axis. As the waves move towards you, which wave peak arrives first?

Also note that the x=0 location is arbitrary. That wave has no beginning, it comes from x → -∞ and goes to x → +∞

 

[nasu]

Edit:

If the x-axis is time, then P will lead Q since P starts earlier?

Yes.

 

[Steve4Physics]

I thought since the wave is moving to the right, P started first compared to Q (the crest of P is closer to y-axis compared to Q). Why is the correct answer B?

Thanks

Edit:
Wait, is it because the x-axis is position so the position of Q is in front of P (more to the right)?
If the x-axis is time, then P will lead Q since P starts earlier?

Say we have a transverse wave, moving in the +x direction, along a string.

There are 2 very different types of graph and it’s easy to get them confused.

I) A displacement-position (d-x) graph. This shows the shape of the wave. It’s basically a 'snapshot', showing the shape of the wave taken at some moment in time.

ii) A displacement-time (d-t) graph. This shows you how the displacement of single particle on the wave, at a fixed x-position, changes over time.

The graph in the Post #1 question is type i) – it’s a snapshot of 2 waves taken at the same moment. The waves are moving right; the wave labelled Q is clearly ahead (further to the right) of wave P. So we can say wave Q leads wave P (by a distance which is 1/8th of a wavelength).

If the graph were type ii), this would show that particle P reaches its (for example) maximum displacement at an earlier time than particle Q reaches its maximum displacement. We would describe this by saying ‘particle P leads particle Q’ (by 1/8th of a period).

Minor edits.

 

[songoku]

I understand.

Thank you very much for the help and explanation DaveE, nasu, Steve4Physics