Video Transcript
A submarine’s sonar scanner uses
sound waves that reflect from objects around the submarine. The submarine emits sound waves
vertically downward and detects their reflection 6000 milliseconds later. The sea beneath the submarine is
4713 meters deep. What is the speed of the sound
waves? Answer to the nearest meter per
second.
Okay, so we have this
submarine. And we’re told that it emits sound
waves vertically downward. We know that the way sonar works is
when these sound waves run into something — in this case the seafloor — they’ll
bounce back and be received by the source that emitted them, the submarine. We’re told two things about this
scenario. First that the submarine is 4713
meters above the sea floor and then second we’re told that the time it takes to emit
and then receive back that sonar signal is 6000 milliseconds. Based on this, we want to figure
out what is the speed of the sound waves as they travel through the sea.
To start working toward our
solution, let’s make an assumption. Let’s assume that the speed of the
sound waves is constant as they travel from the submarine to the seafloor and
back. Under that assumption, we can use
the fact that the average speed of an object — we’ll call it 𝑣 — is equal to the
distance the object travels divided by the time taken. Now if we call the speed of the
sound waves we want to solve for 𝑣, then that’s equal to the total distance
travelled by the waves divided by the time taken to travel that distance.
Looking at the waves in our sketch,
we know that they go down 4713 meters until they run into the seafloor and then they
reflect off the floor and go back up that same distance until they reach the
submarine. That means the distance they travel
is two times 4713 meters. And then when it comes to time,
we’re told that the total elapsed time for these reflected sound waves to be
detected by the submarine is 6000 milliseconds. But instead of using units of
milliseconds in our calculation, we’d like to use units of seconds. To make that conversion, we can
recall that 1000 milliseconds is equal to one second. Therefore, 6000 milliseconds is
equal to six seconds.
Now, solving for wave speed 𝑣 just
involves calculating this fraction: two times 4713 meters divided by six
seconds. To the nearest meter per second, 𝑣
is 1571 meters per second. That’s the speed of this sound wave
through the sea.
