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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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1. 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. 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. 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.