A submarine can use sonar (sound traveling through water) to determine its dista

Question

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 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 sent out pings every 4.20 s, and your apparatus receives echoes reflected from an undersea cliff every 4.19 s, how fast is your submarine approaching the cliff?

Explanation / Answer

Let it is approaching with velocity v.

frequency received by cliff f1= fo*Vs/(Vs-v)

frequency received back f2 = f1*(Vs+v)/Vs = fo*(Vs+v)/(Vs-v)

1/4.19 = 1/4.20 * [1522+v]/[1522-v]

4.20/4.19 = [1522+v]/[1522-v]

[1522-v]*1.002387 = 1522+v

v*(1+1.002387) = 1522*(1.002387-1)

v = 1522*(1.002387-1)/(1+1.002387)

= 1.814 m/s answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.