Question

An ultrasonic wave is sent from a ship towards the bottom of the sea. It is found that the time interval between the sending and receiving of the wave is 1.6 seconds. What is the depth of the sea if the velocity of sound in seawater is 1400 metres per second?
(A) 1120 m
(B) 560 m
(C) 1400 m
(D) 112 m

Answer 1

Hint:Numerical problems involving ultrasonic sound waves can be solved easily by using properties of SONAR waves in water. The speed of SONAR waves and time taken for them to return back can be used to calculate the depth of the sea.

Formula Used:The formula for obtaining the depth of a sea using SONAR waves is as follows:
$s = \dfrac{{2d}}{t}$ Here 2d is the total distance travelled by the wave and t is the time taken by the wave to return back. ‘S’ represents the speed of sound waves.

Step by step solution:
In the given question $s = 1400m{s^{ - 1}}$, $t = 1.6s$
Thus, $1400m{s^{ - 1}} = \dfrac{{2d}}{{1.6}}$
$2d = 1400 \times 1.6$
The term$2d$denotes the distance travelled by the sound wave. The distance or the depth of the sea is $d$.
Thus, $d = 1120m{s^{ - 1}}$
Thus, the depth of the sea as calculated by the SONAR waves is$1140m{s^{ - 1}}$.

Additional Information: SONAR stands for SOund Navigation and Ranging. This technique is based on the echo of sound waves and provides information about the depth of rivers and oceans. More advanced forms of SONAR are used to map ocean beds and find the quantity of fishes and marine animals. The numerical problems given are based on simple forms of SONAR as advanced forms of SONAR are much more complicated.

Note:Students usually mistake using $d$ instead of $2d$. This gives us the total distance travelled by the SONAR wave and not the depth of the sea. This is because the wave takes $1.6s$for bouncing back from the sea bed. This is how SONAR waves are used to calculate the depth of an ocean.