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

Velocity of wave = veolicty of light = 3*10^8 m/s

So frequency of wave of wavelength 1.41 cm = velocity / wavelength = (3*10^8) /(1.41*10^-2) = 2.127659 *10^10 Hz

So , the second frequency is lower,

second frequency = ( 2.127659*10^10) - beat frequency = ( 2.127659*10^10) -(170*10^6) = 2.110659 *10^10 Hz

So, wavelength of second wave = velocity / frequency = (3*10^8)/(2.110659 *10^10) = 1.4213*10^-2 m = 1.4213 cm is the answer