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 the receiving of the wave is $1.5s$. Calculate the depth of the sea, if the velocity of sound in sea water is $1400{\mathrm{ms}}^{-1}$.

Answer 1

Step 1: Given data:

Time interval $\left(t\right)=1.5sec.$
Velocity $\left(V\right)=1400m{s}^{-1}$

Step 2: Formula used:

$d=v\times t$
Where $v$ is the velocity, $t$ is the time interval, $d$ is the distance traveled by ultrasonic waves during $1.5s$

Step 3: Calculating the depth of the sea:

Let, the Depth of the sea is x,

Distance traveled by a sound wave$=2d,$

Time is taken by sound to travel both ways$=1.5s$

$Speedofthesound=\frac{totaldis\tan cetraveled}{timetaken}$

$$\begin{gathered} 1400=\frac{2d}{1.5} \\ d=\frac{1400\times 1.5}{2} \\ d=1050m \end{gathered}$$

Hence, the depth of the sea is $1050m$