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Is there constructive or destructive interference?

  1. Aug 20, 2015 #1
    1. The problem statement, all variables and given/known data

    Two sound sources are coherent and in phase. Is there constructive or destructive interference at the midpoint between the speakers?

    2. Relevant equations

    Generally, there is constructive interference whenever the path-length difference is an integer times the wavelength.

    3. The attempt at a solution

    At the midpoint between the speakers, the path-length difference is zero, which corresponds to constructive interference.

    However, can we apply the usual conditions for constructive and destructive interference to points between the speakers? Sound is a longitudinal wave. Consider the midpoint between the speakers and apply the superposition principle. At the midpoint, away from one speaker is toward the other. Thus, at a given time at this point, if the molecular motion due to one speaker is in one direction, the molecular motion due to the other will be in the opposite direction. Do we not, then, have destructive interference at the midpoint?
     
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  3. Aug 20, 2015 #2

    Bystander

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    "In phase" means "in phase."
     
  4. Aug 20, 2015 #3
    Yes, the sources are in phase. Is that a vote for constructive or destructive interference at the midpoint? According to the superposition principle, there will be no displacement at the midpoint.
     
  5. Aug 20, 2015 #4

    Bystander

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    "In phase" means "in phase," and "yes, it's constructive interference" means "it's constructive interference."
     
  6. Aug 20, 2015 #5

    Bystander

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    You have stated that the sources are in phase, that is, that the compressions and rarefactions of one source are matched by the compressions and rarefactions of the second source; you are interested in constructive or destructive interferences at the midpoint between the sources. The times required for travel of the compression (or rarefaction) fronts from the sources to that midpoint are equal.
     
  7. Aug 20, 2015 #6
    Yes, the sources are in phase. That is, the diaphragms of each speaker move in a synchronized way, so that when the diaphragm of one speaker is moving outward, then so is that of the other speaker, etc.

    The times required to travel to the midpoint will be the same, as you state. However, upon arriving at the midpoint, the molecular motion due to one speaker will be opposite in direction to that of the other. According to the superposition principle, then, the net molecular motion at the midpoint will be zero. This, to me, suggests destructive interference, not constructive.
     
  8. Aug 20, 2015 #7

    ehild

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  9. Aug 20, 2015 #8
    The superposition principle, on which wave interference is based, makes a definitive statement about the net displacement of the medium when two or more waves are present. Namely--The net displacement of the medium at a particular point and time is the sum of the displacements of the individual waves. Unless we are to abandon the superposition principle, we must start with describing the displacements of the molecules and from that deduce the pressure variations.
     
  10. Aug 20, 2015 #9

    HallsofIvy

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    I'm not sure what your point is but the answer is very simple- if the waves are in phase and the distance to the two sources are equal then the maxima from the two sources will arrive at the same time so this is constructive interference as Bystander said.
     
  11. Aug 20, 2015 #10

    ehild

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    Sound wave is considered a scalar wave - that of pressure. But you can consider it as the displacement of the molecules. Displacement is a vector quantity, and equal displacement means both equal magnitude and direction. If the waves are in phase the air molecules move in the same direction at both source.
    The question is, how you define sources in phase. If you have two tuning forks as sources, you have to hit them from the same direction to get waves in phase. So one will move towards the centre and the other one away from it.
     
    Last edited: Aug 20, 2015
  12. Aug 21, 2015 #11
    My point is that the answer is not simple. I agree that "maxima" will arrive at the midpoint at the same time, but suppose that the wave amplitude is 5 cm. In this case, when two maxima arrive simultaneously, one corresponds to a 5 cm displacement in one direction, while the other corresponds to a 5 cm displacement in the opposite direction. According to the superposition principle, then, there is a net displacement of zero at the midpoint.
     
  13. Aug 21, 2015 #12
    Coherent, in-phase sources is standards physics terminology. For sound speakers, it means that the diaphragms oscillate with the same frequency and those oscillations are temporally in phase.
     
  14. Aug 21, 2015 #13
  15. Aug 21, 2015 #14

    HallsofIvy

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    No, that's not two "maxima". That's one maximum and one minimum. That is not "in phase" that is "180 degrees out of phase"! "In phase", means that maxima "leave the source" at the same time and so will reach the midpoint at the same time and minima reach the midpoint at the same time. At the midpoint you will have a wave up to 10 cm and down to -10 cm.
     
  16. Aug 21, 2015 #15

    berkeman

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    The amplitude of the sound wave is not measured in cm. It is measured in units of pressure. That is what you are missing. The longitudinal sound wave is alternating high and low pressure areas, that move away from the source. At the midpoint between the facing, in-phase speakers, the high pressure points add to higher pressure as they pass the midpoint, and the low pressure areas make an even lower pressure area as they pass the midpoint.

    Does that help clear up your confusion? :smile:
     
  17. Aug 21, 2015 #16

    berkeman

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  18. Aug 21, 2015 #17
    Respectfully, not at all. Why can't I choose to measure the amplitude of a sound wave in cm rather than rather than pressure units? The answer is that I can, and the superposition principle is framed in terms of displacements, not pressures. There is no superposition principle for pressure, so we must always begin by describing the displacements, then deduce the pressure variations.
     
  19. Aug 21, 2015 #18

    berkeman

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    Sorry, that is just plain wrong and non-physical. Tell you what, if you are convinced, go ahead and put down as your answer on this problem that the sound waves cancel out at the mid-point between the speakers. You will find out that it is the wrong answer. And it's because the sound wave intensity is measured in units of pressure, not displacement of anything.

    Just because the speaker cone moves to create the alternating pressure wave, does not mean that the wave propagates with the same displacement of air molecules...
     
  20. Aug 21, 2015 #19

    Dale

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    Closed pending moderation.

    For what it's worth, why ask a question for which you believe you already know the answer and about which you are unwilling to consider the alternative.
     
  21. Aug 21, 2015 #20

    berkeman

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    OP's question has been answered as best as we can. Thread will remain closed.
     
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