Question

A research historian is interested in finding a sunken treasure in the Atlantic Ocean. She knows that her equipment is only good enough to recover items that are at a depth of 5 000 m or less. The speed of sound through the water is 1 530 m/s. While working, the sonar equipment detects a reflection that is of interest. The echo from the item takes 6.2 s to return to the sonar detector. Will she be able to retrieve this item?

Answer 1

Answer:

Yes, she will be able to retrieve the item

Explanation:

From the question, we are given the following;

Speed of sound through water v = 530m/s

The time it takes the echo to reach the sonar detector t = 6.2s

First, we need to know how far the echo can travel using the formula;

2x = vt

x is the distance from the source of the sound to the reflector

v is the speed of sound

t is the time

Substituting the given values into the formula:

$x=\frac{vt}{2}\\x=\frac{530*6.2}{2} \\x=530*3.1\\x= 1643m$

Since the research historian knows that her equipment is only good enough to recover items that are at a depth of 5 000 m or less and 1643m is less than 5000m, hence she will be able to retrieve the item.

Answer 2

The research historian can retrieve the item.

Sound is a form of mechanical waves, which is a kind of waves that needs a medium to propagate itself and whose kinematic is representative of motion at constant speed. The maximum echo time ($t_{e}$), in seconds, is the distance travelled by waves ($s$), in meters, divided by velocity of sound through the medium ($v_{s}$), in meters per second:

$t_{e} = \frac{s}{v_{s}}$ (1)

Please notice that distance travelled by sound is twice the depth of the sunken object.

If we know that $s = 10000\,m$ and $v_{s} = 1530\,\frac{m}{s}$, then the maximum echo time is:

$t_{e} = \frac{10000\,m}{1530\,\frac{m}{s} }$

$t_{e} = 6.535\,s$

Any sunken object whose echo time is less than 6.535 seconds can be retrieved. As the echo time related to the item was 6.2 seconds, the research historian can be able to retrieve the object.