## GR0877 Problem 46

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**D**) The first minimum is determined by or . Thus, (Hz)

*Found a typo? Comment!*

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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?

Because the amplitude of diffracted light is and this expression (and, therefore, the intensity) vanishes when , , form which we get . The problem asks the first minimum, that is

@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).

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.

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