Problem 13-72 Double source interference - Part 2

An interference pattern using microwaves of wavelength \(3.0\; cm\) is set up in a physics laboratory. (Microwaves are part of the electromagnetic spectrum; they travel at a speed of \(3.0 \times 10^8\; m/s\) in air.) Two sources of in-phase waves are placed \(18 \;cm\) apart and a receiver is located \(4.8\; m\) away from the midpoint between the sources.
(a) What is the frequency of the microwaves? Express your answer in megahertz \((MHz)\) and gigahertz \((GHz)\).
(b) As the receiver is moved across the pattern parallel to an imaginary line joining the sources, what is the distance between adjacent maxima, between adjacent minima, and between a maximum and an adjacent minimum?

[Ans. (a) \(10000\; MHz; 10\; GHz\)  (b) \(0.80\; m; 0.80\; m; 0.40\; m\) ]

Accumulated Solution

\(v = f\lambda \; \text{or} \; f = v/\lambda = (3.0 \times 10^8\; m/s)/( 3.0 \times 10^{-2} \; m) = 1.0 \times 10^{10}\; Hz = 10\; GHz = 10000 \; MHz\)

Let's make a drawing of the situation. Which is correct?

Three possible wavelength situations; A, B, C.