A submarine, 608m below sea level, sends a SONAR signal to detect an aircraft directly above it. If it receives the signal 10 sec. later, how far the aircraft from the submarine? (Speed of sound in air = 340 m/s, Speed of sound in seawater = 1520 m/s)
Answers
Answer:
A submarine can use sonar (sound traveling through water) to determine its distance from other objects. The time between the emission of a sound pulse (a “ping”) and the detection of its echo can be used to determine such distances.
Alternatively, by measuring the time between successive echo receptions of a regularly timed set of pings, the submarine’s speed may be determined by comparing the time between echoes to the time between pings.
Assume you are the sonar operator in a submarine traveling at a constant velocity underwater. Your boat is in the eastern Mediterranean Sea, where the speed of sound is known to be 1522 m/s. If you send out pings every 2.00 s, and your apparatus receives echoes reflected from an undersea cliff every 1.98 s, how fast is your submarine traveling?
Here's my solution: note it is wrong
Let the submarine be at origin and the cliff be at some point on x axis.
Time taken for the ping to reach the cliff= 2 sec.
In that time the submarine moves 2v distance on x axis (v-velocity of submarine)
Time taken for the echo to reach the submarine=1.98 sec.
In that time the submarine moves 1.98v distance further.
Distance of cliff from origin =1522*2 m
Distance of cliff from submarines final position = 1522*1.98 m
Thus, 2v + 1.98v + 1522*1.98 = 1522*2
V= 7.65 m/s