**Part A**

At point A, there is destructive interference.

Destructive interference is expressed as:

$\overline{){{\mathbf{x}}}_{{\mathbf{A}}}{\mathbf{=}}{\mathbf{(}}{\mathbf{n}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{)}}{\mathbf{\lambda}}}$

At point B, there is constructive interference, expressed as:

$\overline{){{\mathbf{x}}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{n}}{\mathbf{\lambda}}}$

You are listening to the FM radio in your car. As you come to a stop at a traffic light, you notice that the radio signal is fuzzy. By pulling up a short distance, you can make the reception clear again. In this problem, we work through a simple model of what is happening.

Our model is that the radio waves are taking two paths to your radio antenna:

- the direct route from the transmitter
- an indirect route via reflection off a building

Because the two paths have different lengths, they can constructively or destructively interfere. Assume that the transmitter is very far away, and that the building is at an a 45° angle from the path to the transmitter.

Point A in the figure is where you originally stopped, and point B is where the station is completely clear again. Finally, assume that the signal is at its worst at point A, and at its clearest at point B.

Part A

What is the distance d between points A and B?

Express your answer in wavelengths, as a fraction.

Part B

Your FM station has a frequency of 100 megahertz. The speed of light is about 3.00x10^{8} meters per second. What is the distance d between points A and B?

Express your answer in meters, to two significant figures.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Wave Interference concept. You can view video lessons to learn Wave Interference. Or if you need more Wave Interference practice, you can also practice Wave Interference practice problems.

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Based on our data, we think this problem is relevant for Professor Velissaris' class at UCF.