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Question: A sonar device on a submarine sends out a signal and receives an echo \( 5 \) sec later. Calculate t...

A sonar device on a submarine sends out a signal and receives an echo 55 sec later. Calculate the speed of sound in water if the distance of the object from the submarine is 36253625 m.

Explanation

Solution

An echo is heard when the signal travels back in the same direction. We can use the relation between the distance, speed and time for this problem.

Formula used: Use v=stv=\dfrac{s}{t} where ν\nu is the velocity of the object, ss is the distance traveled and tt is the time taken by the object.

Complete step-by-step answer:
An echo is heard when the signal hits any different medium and travels back in the same but opposite direction. Here, the distance travelled by the signal must be doubled as we are dealing with the term echo. So the total distance taken in the formula will be doubled.
Let ss be the distance travelled by the signal. Therefore total distance will be 2s2s . Time taken by the signal to reach the starting point is tt and the speed of sound is vv .
We get,
v=2stms−1 v=2∗36255ms−1 v=1450ms1 \begin{aligned} & v=\dfrac{2s}{t}m{{s}^{-1}} \\\ & v=\dfrac{2*3625}{5}m{{s}^{-1}} \\\ & v=1450m{{s}^{1}} \\\ \end{aligned}
Hence, the speed of the sound in water is 1450ms−11450m{{s}^{-1}} .

Additional Information: An echo is heard when the sound travelling in a direction hits any surface or medium and reflects back towards the source. In modern days, an echo is used for medical purposes. It is also used in determining or estimating the distance, size, and shape. Echo is used to find out the depth of the water bodies. A sonar device is used to find out the objects present under the water bodies. It sends out pulses of waves so, when the waves hit the objects, the waves come back and the device measures how deep or how far is the object present. Similar to sonar devices are Fathometer which are used to find the depth of water.

Note: Make sure to double the distance traveled by the sound wave when calculating the speed of the sound. When the term echo is given in the question, keep in mind that, to hear an echo, sound must travel double the distance.