Question

A car is moving at a speed of $72\text{kmph}$ towards a hill. Car blows a horn at a distance of $1800m$ from the hill. If echo is heard after ten seconds, speed of sound is
$\begin{align}
  & a)300 \\
 & b)320 \\
 & c)340 \\
 & d)360 \\
\end{align}$

Answer 1

Hint: An echo is heard when the sound experiences or hits a different medium and comes back in the opposite direction. The distance travelled by the echo will be double the distance travelled to reach the medium. Convert the speed units into SI systems before solving the formulas.
Formulas used:
$\begin{align}
  & s=ut \\
 & \\
\end{align}$

Complete step-by-step solution:
The above diagram shows how an echo is generated when the sound wave hits a substance or a different medium.
Given, the speed of the car is $\begin{align}
  & 72kmph=72\times \dfrac{5}{18}=20m{{s}^{-1}} \\
 & \\
\end{align}$
Distance travelled by the car in the then seconds will be,
$\begin{align}
  & s=ut \\
 & s=10\times 20=200m \\
\end{align}$
Now, the echo travels a distance of $1800+(1800-200)=3400m$ distance. This is because the car also travels some distance when the echo hits the hills and comes back to the car.
Now, the speed of the sound can be calculated using;
$v=\dfrac{d}{t}=\dfrac{3400}{10}=340m{{s}^{-1}}$
Therefore, the correct option is option c.

Additional information:
An echo is a reflection of the sound that arrives at the listener with a delay after the actual sound. The delay occurring in the sound will be directly proportional to the distance between the source and the reflecting surface. Best examples for echo are produced by the bottom of the well, in a tunnel, when mountains are present, in a closed and empty room. The word echo is a Greek word which means sound. Echo is used by some animals for locating, sensing and navigation like dolphins and whales and bats. An echo is also used to find out the depth of the oceans, presence of any materials in the oceans and seas, to know the depth of the wells etc.

Note: The distance travelled by the sound is taken twice because the echo travels towards the medium, and after getting reflected it travels the same distance in the opposite direction. Therefore, it is taken as twice the distance.