Question

An echo will be heard if the minimum distance between the source of the sound and the obstacle is
$$\begin{gathered} (a)\text{ 1m} \\ (b)\text{ 10m} \\ (c)\text{ 15m} \\ (d)\text{ 17m} \end{gathered}$$

Answer 1

Hint – In this question use the concept that an echo will be heard if the sound waves come to us after getting reflected by the obstacle in 0.1 sec. So let the distance between the source of the sound and the obstacle be x meters, so for an echo the sound waves has to travel twice of this distance. Use the direct relationship between distance, speed and time. This will help getting the answer.

Complete step-by-step answer:
As we know that the speed of sound in air is approximately 340 m/s.
And we all know that whenever we hear a sound it will remain in our mind till 0.1 sec.
Now whenever a sound is generated by the source it travels in the air as a sound wave then it will be reflected by the obstacle after some distance.

So if we want to hear an echo the sound wave will have to come to us after being reflected by the obstacle in 0.1 sec.

Now let the distance between the source of the sound and the obstacle be x meter.
So the sound wave has to travel twice of this distance i.e. 2x meter.
Now as we know the relation between speeds (v), distance (d) and time (t).
As distance is the product of speed and time.
$\Rightarrow d=v\times t$ meters.................. (1)

So this distance i.e. 2x meter will be equal to the speed of sound multiplied by the time i.e. 0.1 sec.

Therefore, distance d = 2x, v = 340m/s and t = 0.1 sec.
Now from equation (1) we have,

Therefore, $2x=340\times 0.1$
$\Rightarrow x={\displaystyle \frac{34}{2}}=17$ Meter.

So the minimum distance between the source of the sound and the obstacle is 17 meter.
So this is the required answer.
Hence option (D) is the correct answer.

Note: Echo is basically termed as the sound waves that are reflected back to the listener by some reflecting objects. For example, it’s common to notice the sound waves coming back from the mountains in hilly regions. Sometimes an echo can be heard of footsteps due to the reflecting marble of an empty hallway.