A ship sends a SONAR signal and receives the reflected sound after 45 seconds. How deep is the ocean? Assume the speed of sound in water to be 1500 m/s.
Answers
Answer:
Explanation:
Velocity of sound in water v=1500 m/s
Let the depth of sea be x.
The sound has to travel to the bottom of the sea and get reflected back to the ship itself, thus total distance traveled by the sound is 2x.
Time taken to hear an echo t=45s
So, 2x=vt
Or 2x=1500×45
⟹ x=33750 m
Given:-
→ Time after which the sound is reflected
back = 45 seconds
→ Speed of sound in water = 1500m/s
To find:-
→ Depth of the ocean.
Solution:-
Let the depth of the ocean be 'd' metres. It will be equal to the distance travelled by the wave in 45 seconds.
We know that :-
If 'd' is the distance of the ship from the deepest point of the sea, then total distance travelled by the wave in time interval t is 2d.
∵ Speed = Distance/Time
=> v = 2d/t
=> vt = 2d
∴ d = vt/2
Where :-
• d is depth of the sea
[distance travelled by the wave in
given time]
• v is speed of sound.
• t is time interval.
=> d = 1500×45/2
=> d = 750×45
=> d = 33750 m
∵ The wave travels a distance of 33750m
in 45 seconds.
∴ Depth of the sea is 33750m .