Oxford PAT 2012, Question 19

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12 thoughts on “Oxford PAT 2012, Question 19

  1. I am still not sure I totally understand the question but I am going to kinda just rephrase what I think you said to check if I know it….. So each time the path difference between reflected waves and waves just emitted is n(lambda), there is constructive interference between them. This means it occurs for path differences of many different values of n, for example 1,2,3 etc… so 2d (distance travelled by reflected waves) = n = )1 or 2,3…. etc.)*(lambda) and d is half that, so the difference between any one of these is (lambda)/2?

    Okay, that aside, I am not quite sure exactly how the microphone detects the maxima and when. The maximum is produced at the speaker isn’t it? Does this resultant wave travel to the microphone or not..? I have seen some answers in terms of standing waves which have really confused me. Yours has really helped but there are just a few oddities in my thinking. Also, is the significance of the speed of the wall being so slow that there is no noticeable Doppler shift that will prevent the waves from being cohesive?

    1. Sorry my description here is a bit terse, so I’m going to flesh it out a little bit. The loudspeaker transmits sound ‘in all directions’. Most of this sound never reaches the microphone, but sound that travels in two directions does reach the microphone: first, the sound that goes straight there; second, the sound that bounces off the screen. These two waves interfere like all waves do. If the microphone is a distance D from the speaker and the screen is a distance d from the speaker, then the direct and reflected waves travel a distance D and (D+2d) respectively to reach the microphone. The waves constructively interfere when they are in phase, i.e. when 2d = nλ. It’s as simple as that.

      The question says that the screen moves ‘slowly to the right’, indicating that speed is effectively zero, so you should ignore the Doppler effect. I don’t find it interesting or useful to think about standing waves to solve this question, but maybe some other analysis does…

  2. hi , for this question i know there is a formula of x= lambda (d)/D, where x is the distance between bright fringe, but how do u get 2d =n lambda???

      1. Yes exactly, the path difference is 2d and therefore there is constructive interference when 2d = nλ, where n is n integer. That is, when the reflected wave has travelled a whole number of wavelengths.

  3. Hello, as I study optics, I am confused by the idea of calculating the maximum intensity of the fringes based on the relative phases of the waves. I understand constructive and destructive interference in the general sense, but how do you find when the wave is in phase and when they are out of phase?

    In my textbook, it says that the difference in path lengths (delta l)=mlambda for constructive (m is an integer). and (delta l)=(m+1/2)lambda for destructive. I am not really sure what these mean in terms of relating the numerics to interference and how to utilize it for out of phase vs in phase…

    Sorry for the rather general question! Thank you so much for this website 🙂

  4. Hi i was wondering for the second part, i can understand part a but i couldn’t get a grip on part b. I thought that there is a series of standing waves established behind the speaker, and thus when the microphone was moved along the x-axis, it would progress from an antinode to a node and back to the antinode again. Is it correct to say so? thks ><

    1. Hi Lee, thanks for your question. Here is some more detail about the solution: I hope it helps.

      We can assume that the screen is smooth and so reflects the sound such that the angle of incidence equals the angle of reflection. This means you can simplify your reasoning by observing that you only need to consider signals travelling along the line that joins M and L. So we can consider the reflection at the screen as being like a point source at the intersection of the screen and the line joining M and L. Since the loudspeaker is a point source too, the whole situation is equivalent to two point sources of sound on a line and a microphone on the same line, and this is equivalent to two co-located point sources that are out pf phase with each other (with the phase being decided by the distance between them).

  5. Yes you are right — it should read as follows:

    Maximum intensity when we have constructive interference, i.e. 2d = n lambda for integers n.

    => d = n lambda / 2 => distance between maximal intensity points = lambda / 2

    Slip of the pen: I wrote: d = n lambda / d by mistake, but then the rest of the answer is right.

    Thanks for pointing it out!

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