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GR0877 Problem 46

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) The first minimum is determined by d \sin{\theta} = \lambda or d \sin{\theta} = c/\nu. Thus, \displaystyle \nu = \frac{c}{d \sin{\theta}} \approx \frac{350}{0.14 \cdot 0.7} = \frac{500}{0.14} \approx 7 \cdot 500 = 3500 (Hz)

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Categories: 0877 Tags: , , , ,
  1. Everyone's Dummer Than You
    12.10.2011 at 10:22

    Obviously your work here is correct, my question is why is it not dsin(theta)=lambda/2? In your original equation, the lambda should be accompanied by an m term to denote the order of the wave’s diffraction. And if the question asks for the frequency where sound will first disappear, I would think they are asking about 1st order DESTRUCTIVE interference, in which case the relevant equation should be (at least to me) dsin(theta)=(m-1/2)lambda. Plug in 1 for m for 1st order destructive interference to get the equation I asked about initially. My thought process here is not correct because it yields answer B, but any ideas as to where I went wrong?

    • 12.10.2011 at 11:27

      Because the amplitude of diffracted light is \displaystyle A_0 \frac{\sin[(d \pi /\lambda)\sin{\theta}]}{(d \pi/ \lambda)\sin{\theta}} and this expression (and, therefore, the intensity) vanishes when (d \pi/\lambda) \sin{\theta} = n \pi, n = 1,2,3, \dots, form which we get d \sin{\theta} = n \lambda. The problem asks the first minimum, that is n = 1

  2. PineApple
    15.10.2011 at 00:10

    @Everyone’s Dummer Than You: the m-1/2 formula for destructive interference is true for INTERFERENCE, that is, light passing through narrow slits. In this case, however, the waves are passing through a wide aperture (diffraction).

  3. Arturodonjuan
    29.08.2016 at 06:36

    For those who didn’t remember which formula to use, or even how to solve this at all, look at the numbers: If we assume the slit width matters, then we know the answer has something to do with the number 14, or, if there’s a factor of 1/2 in the problem, the number 7. Answer (D) is the only one that has a factor of 7 in it.

  4. 18.10.2016 at 22:15

    The arithmetic, in my opinion, is easier if you recognize that 0.14 is Sqrt(2)/10. Then d sin(45) is 1/10.

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