Question

A sonar device fitted in a submarine receives an echo $4{\rm{ s}}$ later the signal is transmitted towards another submarine $3060{\rm{ m}}$ away. Find the speed of sound in water.
A. $1530{\rm{ }}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}$
B. $1342{\rm{ }}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}$
C. $1600{\rm{ }}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}$
D. $1250{\rm{ }}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}$

Answer 1

Hint: In the solution we use the basic relation between speed, distance, and time to find the speed of sound in water using the given values of time and distance.

Complete step by step answer:
Given:
Total time taken by echo to reach the submarine $t = 4{\rm{ s}}$
Distance between the submarines $d = 3060 {\rm{ m}}$
The relation between speed, distance, and time is given by
$v = \dfrac{D}{t}$
Where $v$ is the speed and $D$ is the total distance travelled.
Given the signal is transmitted to another submarine and its echo is recorded, that means the signal travelled $3060 {\rm{ m}}$ on its way to the another submarine and its echo has travelled another $3060 {\rm{ m}}$ in order to reach the source submarine.
Therefore, the total distance travelled is
$
D = 2 \times 3060{\rm{ m}}\\
\Rightarrow D = 6120{\rm{ m}}
$
Substituting the values of total distance travelled and the time taken in above equation gives
$
v = \dfrac{{6120{\rm{ m}}}}{{4{\rm{ s}}}}\\
\therefore v = 1530{\rm{ }}{{\rm{m}} {\left/
{\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}
$
Therefore, the correct answer is option A that is $1530{\rm{ }}{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.} {\rm{s}}}$.

Note: Make sure to take total distance travelled by the sound into account and not just the distance between the submarines.Moreover,sonar stands for sound navigation ranging. It is defined as the technique used for determining the distance and direction of underwater objects with the help of sound waves. This technique is used by animals such as bats and whales.