A rock under water is 1595m deep. Find the time in which an ultrasonic signal returns after reflection from the rock. Given speed of ultrasonic waves in water = 1450ms⁻¹.

The correct option is 2.2 s.

Understanding the Physical Concept:
When an ultrasonic signal is transmitted from the water surface, it travels downwards to the rock, reflects off it, and travels back up to the receiver. Since the signal covers the depth of the water twice (once going down and once coming up), the total distance ($D$) traveled by the signal is twice the depth ($d$) of the rock.

$D=2d$

Given Data:
Depth of the rock under water ($d$) = 1595 m
Speed of ultrasonic waves in water ($v$) = 1450 m s^-1

Step-by-Step Calculation:
The relation between speed, total distance, and time taken ($t$) is given by the formula:

$\mathrm{Speed}\left(v\right)=\frac{\mathrm{Total\; Distance}\left(D\right)}{\mathrm{Time\; Taken}\left(t\right)}$

Substituting the total distance $D=2d$ into the equation:

$v=\frac{2d}{t}$

Rearranging this equation to solve for the time ($t$):

$t=\frac{2d}{v}$

Substitute the given values into the rearranged formula:

$t=\frac{2\times 1595}{1450}$

Calculate the total distance traveled in the numerator:

$2\times 1595=3190\text{m}$

Now, divide by the speed of the wave to find the time:

$t=\frac{3190}{1450}=2.2\text{s}$

Thus, the time in which the ultrasonic signal returns after reflection is 2.2 seconds.