Question

A submarine emits a sonar pulse, which returns from an underwater cliff in $1.02s$ . If the speed of sound in salt water is $1531m{\text{ }}{{\text{s}}^{ - 1}}$ , how far away is the cliff?

Answer 1

To answer this question, we must know how sonar works and after just putting the values in the equation we will get the answer. Sonar is a technique that uses sound propagation to navigate, communicate with or detect objects on or under the surface of the water, such as other vessels.
{\text{Speed of sound}} = \dfrac{{{\text{Distance travelled by sound}}}}{{{\text{Time taken}}}} \\\ \Rightarrow v = \dfrac{{2d}}{t} \\\
Where,
$v$ is the speed of sound in water,
$t$ is the time taken by the sound to return and
$d$ is the distance travelled by the sound.

Complete answer:
Here it is given that,
$t = 1.02s \\\ v = 1531m{\text{ }}{s^{ - 1}} \\\ \because v = \dfrac{{2d}}{t} \\\ \therefore d = \dfrac{{v \times t}}{2} \\\ \Rightarrow d = \dfrac{{1531 \times 1.02}}{2} \\\ \Rightarrow d = \dfrac{{1531 \times 102}}{{2 \times 100}} \\\ \Rightarrow d = \dfrac{{156162}}{{200}} \\\ \Rightarrow d = 780.81m$
Hence, the distance between the submarine and the cliff is $780.81m$ .

Additional Information:
SONAR stands for Sound Navigation and Ranging. SONAR is a process of communicating or detecting objects underwater. It is generally used by ships, submarines to detect underwater objects like rocks, icebergs which cause serious risk to the ships. Submarines also communicate with the help of SONAR and during wars military ships and submarines and detect underwater torpedo and missile attack with the help of SONAR. So, it serves for plenty of uses but let us first understand the working of SONAR.

Note:
Do not confuse $d$ and $2d$ . We use $2d$ because we take total distance as the total distance covered by the ultrasonic wave i.e., from transducer to object and back from object to detector. SONAR works using ultrasonic waves. A transmitter and receiver are used in SONAR techniques. The whole device has been loaded into the ship. Ultrasonic waves or ultrasound are generated by the transmitter. These waves travel across water. Waves pass through water and hit objects submerged or on the seabed. These waves are reflected by objects or the seabed after they strike. As a result, the receiver collects these waves. The ultrasonic waves are then converted into electrical signals, which are studied to determine underwater conditions and obstacles.