Question: How far away should a deep sea diver be from an under-sea rock so that he can hear his own echo? (Sp...

Question

How far away should a deep sea diver be from an under-sea rock so that he can hear his own echo? (Speed of sound in water is $1500m/s$ )
A. $1500m$
B. $750m$
C. $150m$
D. $75m$

Answer 1

Solution

Here, we need to consider the condition necessary for us to experience an echo. Once we do that, we can easily substitute the values given in the proper formula and obtain the answer.

Formula used
$d = v \times t$ where $v$ is the velocity of sound in water, $t$ is the time taken by the sound wave to get reflected back to the diver and $d$ is twice the distance between the diver and the under-sea rock.

Complete step by step answer
Echo is an acoustic phenomenon where a sound wave is reflected back to the source. When a sound wave or an echo itself is reflected multiple times then it is characterized as a reverberation. Usually to perceive an echo the source must be enclosed in a closed space large enough for our ears to detect the delay.
The sensation of sound persists in our brain for about $0.1s$ . So, for us to be able to detect an echo, the sound must take a minimum of $0.1s$ to travel and get reflected back.
So, the minimum amount of time taken for the diver to hear back his own echo under the sea should be $0.1s$ .
Therefore, the distance between the diver and the sea-rock is
$d = v \times t$ where $v$ is the velocity of sound in water and $t$ is the time taken by the sound wave to get reflected back to the diver.
$\begin{gathered} \Rightarrow d = 1500 \times 0.1 \\\ \Rightarrow d = 150m \\\ \end{gathered}$
This is the total distance transversed by the sound wave travelling from the diver to the sea rock and back.
So, the minimum distance between the diver and the sea rock must be half of this value, which is
$\dfrac{{150}}{2} = 75m$

Therefore, the correct option is D.

Note: A true echo is a single reflection of the sound source. Also, if the sound is reflected back before $0.1s$ our brain will not be able to differentiate it from the original sound. That is why we are not able to perceive echo in small spaces or in our homes.