Oxford PAT 2012, Question 19

2012_page17

9 thoughts on “Oxford PAT 2012, Question 19

  1. 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.

  2. 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 🙂

  3. 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).

  4. 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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