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Homework Help: Wave Problem (constructive interference)

  1. Mar 13, 2006 #1
    Hey everyone,

    here's a problem that's been troubling me all day and I really have no idea what else to do:

    "Speakers A and B are vibrating in phase. They are directly facing each other, are 8.0 m apart, and are each playing a 76.0-Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are three points where constructive interference occurs. What are the distances of these three points from speaker A?"

    I've found the wavelength (using v=343 and f=76) to be 4.513.

    I then set up three equations, that I think in theory will give me the right answer:
    (w = wavelength)
    (l = length (8m))

    x=w
    l-x=3w

    y=2w
    l-y=2w

    z=3w
    l-z=w

    However, when I submitted this each answer online, I got an incorrect answer. Any help would be appreciated. thanks in advance,

    Sam
     
  2. jcsd
  3. Mar 13, 2006 #2

    nrqed

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    Homework Helper
    Gold Member

    There is no reason to impose that you are at a distance w from one speaker!! You could be at 1.3 w, or 0.668w or any other distance!
    (btw, notice that your solution would work only if l = 4 w which is not the case here).
    What you must do is to impose that the difference of distance travelled by both waves is either 0 or w or 2w and so on.

    Call x the distance from the first speaker. Then l-x is the distance from the second speaker (as you already had). Then impose that the difference between the two distances is 0 or w or 2 w, etc.

    so

    l-x - x = 0, w, 2w , ect.

    The first possibility gives you the obvious solution: right in the middle. Then you will get the others. Of course, no solution is possible when n w gets above l, which happens for the first time when n =3. so l- 2x = 3 w has no solution in your case. This shows that there are only 3 solutions (corresponding to 0, w and 2w)

    Pat
     
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