Question

Radar uses radio waves of a wavelength of 2.4 \({\rm m}\) . The time interval for one radiation pulse is 100 times larger than the time of one oscillation; the time between pulses is 10 times larger than the time of one pulse. What is the shortest distance to an object that this radar can detect? Express your answer with the appropriate units.

Answer 1

120 m

Step-by-step explanation:

Given:

wavelength 'λ' = 2.4m

pulse width 'τ'= 100T ('T' is the time of one oscillation)

The below inequality express the range of distances to an object that radar can detect

τc/2 < x < Tc/2 ---->eq(1)

Where, τc/2 is the shortest distance

First we'll calculate Frequency 'f' in order to determine time of one oscillation 'T'

f = c/λ (c= speed of light i.e 3 x
`10^(8)` m/s)

f= 3 x
`10^(8)` / 2.4

f=1.25 x
`10^(8)` hz.

As, T= 1/f

time of one oscillation T= 1/1.25 x
`10^(8)`

T= 8 x
`10^(-9)` s

It was given that pulse width 'τ'= 100T

τ= 100 x 8 x
`10^(-9)` => 800 x
`10^(-9)` s

From eq(1), we can conclude that the shortest distance to an object that this radar can detect:

`x_(min)`= τc/2 => (800 x
`10^(-9)` x 3 x
`10^(8)`)/2

`x_(min)`=120m