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Compressional wave impulses are sent to the bottom of sea from a ship and the echo is heard after 4s. If bulk modulus of water is $2\times {{10}^{9}}N{{m}^{-2}}$ and the mean temperature is ${{4}^{\circ }}C$, then depth of the sea is
$\begin{align}
  & \left( A \right)2000\times {{10}^{3}}m \\
 & \left( B \right)2828m \\
 & \left( C \right)1414m \\
 & \left( D \right)707m \\
\end{align}$

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Last updated date: 13th Jun 2024
Total views: 393k
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Answer
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Hint: For calculating the depth of the sea , consider the concept that time is the ratio of displacement to the velocity. Let us assume the distance is 2d. That is, the initial distance before echo is d and after echo also the sound waves travels a distance d. Then the total distance becomes 2d. The depth can also be defined as the square root of bulk modulus to the density of the material. hence we will get the depth of the sea.

Complete answer:
The reflection of sound waves can lead to a production of a similar sound called echoes. The echo sound is heard after 4 seconds after the initial sound is heard. Sometimes when the sound travels from one medium to another, reflection of sound waves occur. Our own sound waves are heard back at the time of echoes. The reflecting surface may be either solid or liquid.
Let us assume the distance is 2d. That is, the initial distance before echo is d and after echo also the sound waves travels a distance d. Then the total distance becomes 2d.
Time taken by the wave is given by,
$\begin{align}
  & \dfrac{2d}{{{V}_{S}}}=2 \\
 & \\
\end{align}$
$\begin{align}
  & \Rightarrow d={{V}_{S}} \\
 & \\
\end{align}$
In the equation below d is the depth of the sea, B is the bulk modulus and $\rho $ is the density of water. Thus by substituting the value we will get the depth of the sea.
$\begin{align}
  & \Rightarrow d=\sqrt{\dfrac{B}{\rho }} \\
 & \Rightarrow d=\sqrt{\dfrac{2\times {{10}^{9}}}{1000}} \\
\end{align}$
$\therefore d=1414m$

Hence, option (C ) is correct.

Note:
Thus reflection of sound waves is otherwise a change in direction of the waves from one medium to another. Some time at the interface between two mediums the waves may reflect back. Sound is a longitudinal wave. It definitely requires a medium to propagate. If the sound waves cannot absorb or transmit through a surface then it will reflect. The initial beam refers to the incident wave and the final wave is the reflected wave.