# Math Help - urgent help please !

1. ## urgent help please !

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2. Originally Posted by kittycat12
question 1
You are driving down the road in your car and you notice that your favorite radio station that you are listening to, 95.7 MHz, is going in and out. You look out and over and you see two long buildings with a gap in them. You know that you are a distance of 100 meters from the buildings. As you pass directly across from the gap in the buildings, you notice that the readio reception is the strongest. From there it continually get worse and worse untill you have traveled 17.6 meters where there is no reception. It then comes back in but goes out agian after traveling 37.1 meters from the center point (19.5 m further down the road), and it goes out agian at 61.1 meters from where you started measuring.
What is the width of the gap between the buildings?

Mr F says: Review the concept of single slit diffraction.

question 2
This is a Michelson-Morley Interferometer (Diagram not part of the question):

Question: A glass container is placed along arm 2 (the arm right above L_A in the diagram) of the interferometer. The glass container is 1 cm long (you may ignore the thickness of the glass).
At first, the container is empty and the mirror along the horizontal line (the mirror that is placed vertically) is adjusted so that a bright fringe is observed at the detector. Now, a gas of unknown index of reflection is slowly allowed to enter to container. During the time this occurs, 1624 changes between bright and dark are observed to occur while it is filling up. The source is known to have a wavelength of 550 nm. What is the index of refraction for this gas?

Mr F offers food for thought: The speed of light in a medium of refractive index n is given by v = c/n where c is the speed of light in a vacuum.

sorry, i hope it is okay to post the physics questions here. i posted these two questions in the physcis forum but only see 4-5 ppl viewing. I need your urgent help for teaching me how to solve them. Please help if you know . thank you very much.
The physics link is here: http://www.physicshelpforum.com/phys...pilcation.html. Question 1 has had several replies.

3. Originally Posted by kittycat12
Thanks for the hint, but the replies in that thread didn't help me much for question 1, I still don't really understand how to do it. I'm left with many thetas and Ds, and I want only one D (the distance between the building)

I know it's single slit, but i'm horrible at that, do you think you can help me a little more please?
You should know that $Y_{\text{min}} = \frac{n \lambda D}{d}$ where d is the width of the slit, $\lambda$ is the wavelength of the waves, D is the distance from the slit to the detector, and n is a positive integer.

Therefore the distance between successive intensity minima is constant and is equal to $\frac{\lambda D}{d}$.

For your problem, you need to find the value of d, given the following data:

$f = 95.7 \times 10^6 \, \text{Hz} \, \Rightarrow \lambda = 3.13 \, \text{metres}$.

$D = 100 \, \text{metres}$

Constant distance between successive intensity minima = distance between n = 1 and n = 2 minima = 19.5 metre ....... no, wait a minute ..... it = distance between n = 2 and n = 3 minima = 24 metre ..... doh!

Now you see what the trouble is ....... Perhaps there's error in the measured distances and you should use an average value ......

Note that the calculated value for the gap (slit width) is not very small compared to the distance between car and buildings (distance between detector and slit) so the above formulae probably only give a rough estimate (which would explain why the distance between successive minima is not constant).

I don't really have the time or the inclination to do an exact calculation where no approximations regarding relative size of slit widths, distances and wavelengths are made. I doubt the question requires you to do this either.