Question

A pulse of sound is produced at the bottom of a boat. The sound travels through the water and is reflected from the sea-bed. The sound reaches the boat again after 1.3 s. The sea-bed is 1000 m below the boat. Using this information, what is the speed of sound in the water?
A) 769 m/sec
B) 1300 m/sec
C) 1538 m/sec
D) 2600 m/sec

Answer 1

Hint:To find the speed of sound we need reference medium, formula for speed of sound is given with respect to gases. It is the square root of the adiabatic expansion of the gas divided by the density of the medium and the coefficient of pressure.
$$\begin{array}{rl}& \text{The mathematical representation is }\\ & v\text{ = }\sqrt{{\displaystyle \frac{\gamma P}{\rho }}}\end{array}$$


Complete step by step solution:
As given in question, boat is above 1000m of sea end so,
$\begin{array}{rl}& \text{Total distance traveled by sound in water }\\ & \text{ = 2 }\times \text{ 1000}\\ & =\text{2000 m}\\ & \text{Total time taken during journey mentioned = 1}\text{.3 sec}\\ & \Rightarrow \text{Speed of sound in water = }{\displaystyle \frac{\text{Total distance traveled by sound in water }}{\text{Total time taken during journey mentioned }}}\\ & \therefore \text{Speed of sound in water = }{\displaystyle \frac{2000}{1.3}}\\ & \therefore \text{Speed of sound in water = 1538}\text{.5 m/sec }\end{array}$

Hence option C is correct

Additional Information:Speed ​​of sound is defined as the dynamic propagation of sound waves. It depends on the characteristics of the medium in which diffusion is taking place. The speed of sound is used to describe the velocity of sound waves in an elastic medium. Sound travels at different speeds depending on what it is experiencing , Of the three sound waves (gas, liquid and solid) sound waves travel more slowly through gas, faster through liquids, and faster through solids. There is a requirement of medium for sound waves to travel and the density of the medium is considered one of the factors on which the speed of sound depends. When the medium is dense, the molecules in the medium are closely packed which means that the sound travels fast. Therefore, the speed of sound increases as the density of the medium increases.
Also, when the speed of any object exceeds the speed of sound waves, the speed of the respective object is known as the supersonic speed. For example, the speed of projectiles, jet aircraft, etc.

Notes:The speed of sound depends on the type and properties of the medium through which it is traveling. The speed of sound in a particular medium depends on the temperature and pressure of that medium. The speed of sound decreases when it passes from the solid to the gaseous state of a given medium.