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Sound wave problem

  1. Jan 24, 2014 #1
    1. The problem statement, all variables and given/known data
    A source of sound S and a detector D are placed at some distance from one another. A big cradboard is placed near the detector and perpendicular to line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 m/s.


    2. Relevant equations



    3. The attempt at a solution
    I have posted a similar problem in the past.
    https://www.physicsforums.com/showthread.php?t=684072&highlight=sound+detector+wall

    (The figure is present in the linked thread. I can't seem to attach it to the current thread :confused: )

    I tried the current problem the following way:

    Let the cardboard be initially at a distance ##x## from S and let D be at a distance ##y## from S. The path difference between the two waves reaching D is ##2(x-y)##. For a maximum, the path difference must be ##n\lambda## i.e ##2(x-y)=n\lambda\,\, (*)## where n is a non-negative integer. When the cardboard is moved by 20 cm, the path difference is ##2(x-y)-40##. For a minimum, this must be a equal to ##(m+1/2)\lambda## where m is a non-negative integer. Using (*), I get:
    $$n\lambda-40=\left(m+\frac{1}{2}\right)\lambda$$
    Solving for ##\lambda##
    $$\lambda=\frac{40}{n-m-1/2}$$
    If I assume ##n=1## and ##m=0##, I get the given answer i.e 420 Hz but if I assume some other values, I get different answers. :confused:

    Any help is appreciated. Thanks!
     
  2. jcsd
  3. Jan 24, 2014 #2
    The key thing is that the path difference between a consecutive maxima and minima is λ/2 .

    Now when the detector is moved 20 cm away ,the path difference introduced is 40 cm .

    i.e 40 = λ/2 or λ = 80cm .

    f=c/λ = 420 Hz .
     
    Last edited: Jan 24, 2014
  4. Jan 24, 2014 #3

    ehild

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    See how you can attach an old picture


    attachment.php?attachmentid=57630&d=1365435100.png

    Or you can attach it again, by changing the name.

    Tania is right, the keyword is "consecutive" n and m differ by one.

    ehild
     
  5. Jan 25, 2014 #4
    Thanks a lot Tanya and ehild! :smile:

    I had a similar dilemma with the other problems I am currently going through but now they are all solved, thanks! :)
     
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