Question

Suppose you are swimming underwater in a lake and a sound is made 1,000 meters away from you. How long would it take for the sound waves to reach your ears? Would they reach you faster or slower if you were swimming in the ocean? Why?

Answer 1

Answer:

0.667 s; faster in the ocean

Explanation:

Since the sound wave travels with a uniform motion (= at constant velocity), the time it takes to reach your ear will be given by the formula

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

where

d is the distance it has to cover

v is the speed of the sound wave

Here we have

d = 1000 m is the distance

v = 1500 m/s is the approximate speed of sound in fresh water

Substituting,

$t=\frac{1000}{1500}=0.667 s$

We also want to compare the time if you are swimming in the ocean.

In the ocean, due to the higher density of the water (because of the presence of the salt), the speed of sound is slightly larger, in fact it is:

$v=1531 m/s$

Therefore, the time taken in this case will be:

$t=\frac{1000}{1531}=0.653 s$

Therefore, the sound will reach your ear a bit faster.