When radio waves try to pass through a city, they encounter thin vertical slits: the separations between the buildings. This causes the radio waves to diffract. In this problem, you will see how different wavelengths diffract as they pass through a city and relate this to reception for radios and cell phones. You will use the angle from the center of the central intensity maximum to the first intensity minimum as a measure of the width of the central maximum (where nearly all of the diffracted energy is found).
Consider radio waves of wavelength λ entering a city where the buildings have an average separation of a.
(A) Find the angle θ to the first minimum from the center of the central maximum (Express your answer in terms of λ and a)
Assume that the average spacing between buildings is a=20 m.
(B) What is the angle θ_FM to the first minimum for an FM radio station with a frequency of 101 MHz? (Express your answer numerically in degrees to three significant figures. Note: Do not write your answer in terms of trigonometric functions. Evaluate any such functions in your working.)
(C) What is the angle θ_cell for a cellular phone that uses radio waves with a frequency of 900 MHz? (Express your answer in degrees to three significant figures.)
(D) What problem do you encounter in trying to find the angle θ_AM for an AM radio station with frequency 1000 kHz?

a) The angle becomes zero.
b) The angle can be given only in radians.
c) To find the angle it would be necessary to take the arcsine of a negative number.
d) To find the angle it would be necessary to take the arcsine of a number greater than one.