Question

Two microwave signals of nearly equal wavelengths can generate a beat frequency if both are directed onto the same microwave detector. In an experiment, the beat frequency is 170MHz . One microwave generator is set to emit microwaves with a wavelength of 1.410cm.
If the second generator emits the longer wavelength, what is that wavelength?

Answer 1

Answer:

The wavelength of the wave is 1.419 cm.

Explanation:

wavelength emitted by the one micro wave = 1.41 cm

beat frequency =  170 M Hz

Let the frequency of the wave is f.

$f=\frac{c}{\lambda }\\\\f =\frac{3\times 10^8}{0.0141}\\\\f = 2.13\times 10^{10} Hz$

Let the frequency of the other wave  is f'.

$f' = 2.13\times 10^{10}-170\times10^6\\\\f' = 21130\times 10^6 Hz$

The wavelength is given by

$f' = 21130\times 10^6 Hz\\\lambda = \frac{3\times 10^8}{21130\times 10^6}\\\\\lambda = 0.01419 m = 1.419 cm$