Question

A RADAR sends a signal to an aeroplane at a distance 45 km away with a speed of $3\times {10}^{8}m{s}^{-1}$. After how much time is the signal received back from the aeroplane ?

• A. $3\times {10}^{-4}s$
• B. $3\times {10}^{-3}s$
• C. $2\times {10}^{-4}s$
• D. $5\times {10}^{-2}s$

Answer 1

The correct option is A $3\times {10}^{-4}s$

Like all waves, sound waves can be reflected. Sound waves suffer reflection from the large obstacles. As a result of reflection of sound wave from a large obstacle, the sound is heard which is named as an echo. Ordinarily echo is not heard as the reflected sound gets merged with the original sound. Certain conditions have to be satisfied to hear an echo distinctly (as a separate sound).
The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off.
As the speed of sound is $3\times {10}^{-3}m/s$ and the distance traveled by sound is 45 m are given in the question, the time taken is calculated from the formula,
$Timetaken=\frac{Distancetraveled}{velocityofsound}$.
The total distance traveled by the sound is given as $2\times 45$ m as it is a reflected sound.
The time taken for the signal to be reflected back from the aeroplane is $=\frac{2\times 45m}{3\times {10}^{-3}m/s}$ = $3\times {10}^{-4}$ seconds.