Question

Plane microwaves from a transmitter are directed normally towards a plane reflector. A detector moves along the normal to the reflector. Between positions of 14 successive maxima, the detector travels a distance 0.13 m. If the velocity of light is 3 × 10 8 m/ s, find the frequency of the transmitter.

Answer 1

The detector moves by a distance, d = 0.14 m

In this distance, there are 14 maxima.

Now, distance between two consecutive maxima is equal to ""half wavelength"".

Hence, we have for 14 maxima

$14\quad \times \quad \frac { \lambda }{ 2 } =\quad 0.14$

$\lambda \quad =\quad \frac { 0.28 }{ 14 } =\quad 0.02\quad m$

Speed of light, $v\quad =\quad 3\quad \times \quad { 10 }^{ 8 }\quad \frac { m }{ s }$

Hence, the frequency of the transmitter is,

$f\quad =\quad \frac { v }{ \lambda } =\quad \frac { 3\quad \times\quad { 10 }^{ 8 } }{ 0.02 }$

$f\quad =\quad 1.5\quad \times \quad { 10 }^{ 10 }\quad Hz$