Understanding Wave Reflection and Phase Shifts

[Dalcier]

I've attached the multiple choice question.

The first time round that I did it, I simply just did a phase shift of the whole graph by pi. Basically I just translated the whole graph by pi, resulting in option (D).

However, it later came to my attention that by continuing to draw the waveform in the medium itself and simply reflecting it just like a mirror, you will get the reflected and pi phase shift, but this gets the answer as option (B), which is still wrong.

Working backward from the answer, it seems as though i have to use both the reflecting and afterwards translating the whole graph by pi in order to get the answer, which is option (C)?

Can anyone explain the mechanics behind the methods of what I'm doing? Or perhaps just an explanation to better understand the mechanics of the wave reflection?

Thank you!

 

[Redbelly98]

Welcome to Physics Forums!

Working backward from the answer, it seems as though i have to use both the reflecting and afterwards translating the whole graph by pi in order to get the answer, which is option (C)?

Yes, that's the one.

Can anyone explain the mechanics behind the methods of what I'm doing? Or perhaps just an explanation to better understand the mechanics of the wave reflection?

Thank you!

Okay, but you pretty much have reasoned it out already. The reasoning is a two step process:

First, take the wave that would be transmitted beyond the surface (as you drew in the figure), and reflect it as if the surface were a mirror.

Second, you apply the given information about the phase to the reflected wave. In this case, shift it by pi because that was given information. We don't know what type of wave this is, so we don't know why there is a phase shift; we're just using the information given to us that there is a phase shift.

A further remark:

The phase-shift information depends on the type of wave, and isn't always pi for every type of wave. For example, if the wave were describing the air pressure then it would not get a shift of pi. On the other hand, if the wave is describing the motion of air molecules, then is does get a pi phase shift.

Hope that helps.