(a) The readings obtained by the receiver R are due to the phenomenon of interference. When the electromagnetic waves from the source O reach the reflector M, they bounce off the metal surface and create reflected waves. When the reflected waves meet the original waves, they interfere with each other. This interference can be constructive or destructive, depending on the path difference between the original and reflected waves.
At certain locations along the line normal to the reflector, the path difference between the original and reflected waves is such that they reinforce each other, leading to constructive interference. This results in the receiver R detecting a maximum reading on the meter. At other locations, the path difference is such that the original and reflected waves cancel each other out, leading to destructive interference. This results in the receiver detecting a minimum reading on the meter.
As receiver R moves between O and M along the line normal to the reflector, the path difference gradually changes, leading to alternating maximum and minimum readings on the meter.
(b) To calculate the frequency of the source O, we can make use of the interferometer equation:
螖x = 位/2
Where:
螖x is the path difference between the original and reflected waves
位 is the wavelength of the electromagnetic waves
In this case, the average distance between successive minima is given as 1.5 cm. Since there is destructive interference at the minima, we know that the path difference between the waves is an odd multiple of half the wavelength. Therefore, we can write:
螖x = (2n + 1)位/2
Rearranging the equation, we have:
位 = 2螖x / (2n + 1)
Given that the speed of electromagnetic waves in air is 3.0 x 10^8 m/s, we can now calculate the frequency (f) of the source O using the formula:
f = v / 位
Substituting the values:
f = (3.0 x 10^8 m/s) / (2螖x / (2n + 1))
f = (3.0 x 10^8 m/s) * (2n + 1) / (2螖x)
Substituting 螖x = 1.5 cm = 0.015 m and assuming n = 0 (since the average distance between successive minima is given), we can calculate the frequency of the source O.