Question

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects underwater. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be \[77.0s\]. What is the distance of the enemy submarine? (Speed of sound in water = $1450m{s^{ - 1}}$).

Answer 1

Hint: The given question is based on a direct formula for the distance with the help of a SONAR. If we remember the formula for finding the distance using a SONAR, then we can easily conclude with the correct solution of the given question.

Complete step by step solution:
The total time of reception and reflection of the echo sent by the SONAR is given to be, $t = 77.0s.$
Also, the speed of sound in water is given to be, $s = 1450m{s^{ - 1}}$
Now, we know the relation of speed, distance and time in case of a SONAR is given by,
$s = \dfrac{{2d}}{t}$
Now, let us put the values of speed and time in the equation given in step one to find the required value of the distance of the enemy submarine.
By putting the values, we will get
$\Rightarrow 1450 = \dfrac{{2d}}{{77}}$
$\Rightarrow 2d = 1450 \times 77$
$\Rightarrow d = \dfrac{{1450 \times 77}}{2}$
$\therefore d = 55825m$
Let us convert the distance in kilometers.
So, we will get, $d = \dfrac{{55825}}{{1000}} = 55.8km$

So, the required distance of the enemy submarine is $55.8km$.

Note: We need to be clear with the concept of using \['2d'\] as the distance in the speed-distance formula. Since, in the case of SONAR, we take the time while the sound wave is sent and again when it comes back. It means the distance travelled to reach the body under water and again the distance travelled when the sound reflects back. That is why we are using $s = \dfrac{{2d}}{t}$ instead of $s = \dfrac{d}{t}$. So, by using a SONAR we can find the depth of objects under water or the depth of sea or river. With the help of SONAR we can send the pulse of energy ranging between $1 - 15cm$ wavelengths.