An echo is returned in $3$ seconds. What is the distance of the reflecting surface from the source given that the speed of the sound is $342\,m/sec$ ?

Hint:Echo is a sound reflection that arrives at the listener with a pause after the direct sound. It is used in audio signal processing and acoustics. The interval between the source and the listener is proportional to the delay of the reflecting surface.

Complete step by step answer:
Let’s assume any source ‘X’ of sound produces a sound and it is found that the echo of the sound was returned in $3$ seconds. It is given that the speed of the sound in which it is travelling is $342\,m/sec$. It means that the sound can travel $342m$ in $1$ second.

Firstly, we will calculate the distance travelled by the sound in $3$ seconds after reflection.Let’s assume that the speed of sound is denoted by $v$ and time in which echo returns is denoted by $t$. The formula to calculate the distance travelled is the product of the speed and the time.It is written as –
Distance = speed $ \times $ time
Or we can write as –
$d = v \times t$
Now, substituting the values, we get –
Distance travelled by the sound = $342 \times 3$
Distance travelled by the sound = $1026\,m$

So, this is the total distance of the sound travelled. It means this is the distance of the sound travelled starting from the source to the reflecting surface and coming back to the source again. It means that in order to calculate the distance from the source to the reflecting surface, we have to divide it by $2$, since this distance is doubled.
The distance of the reflecting surface from the source $ = \dfrac{{1026}}{2} = 513\,m$

Hence,the distance of the reflecting surface from the source is 513 m.

Note: Sound and echo seem to be similar concepts, but are not. They are different phenomena of sound. When the sound is repeated when the sound wave is reflected, it is known as echo. Echo is heard when space is large.