Answer to Question #220395 in Physics for Swagoo

Question

A research historian is interested in finding 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

Find the time required for the sound to travel in one direction assuming the speed of sound is equal back and forth:

$$t=\frac T2.$$

Find the depth:

$$d=ct=\frac{cT}{2}=\frac{1530·6.2}{2}=4743\text{ m}.$$

She will be able to retrieve the items.