Two ships are moving along a line due east (see figure below). The trailing vess

Question

Two ships are moving along a line due east (see figure below). The trailing vessel has a speed relative to a land-based observation point of v1 = 73.0 km/h, and the leading ship has a speed of v2 = 45.0 km/h relative to the point. The two ships are in a region of the ocean where the current is moving uniformly due west at vcurrent = 12.2 km/h. The trailing ship transmits a sonar signal at a frequency of 1,200.0 Hz through the water. What frequency is monitored by the leading ship? (Use 1,533 m/s as the speed of sound in ocean water. Express your answer to five significant figures.) WebAssign will check your answer for the correct number of significant figures. Hz

Explanation / Answer

In this case water will first act as an observer for ship moving with speed v1 then act like a source for ship moving at speed v2, so frequency observed by water -

f = [c+v/c+v'] f0

WHERE v = speed of receiver

v' = speed of source

c = speed of sound in water = 1.53*5/18 = 0.425 km/hr

f = [c+32.8/c+60.8]

speed shown here are observation based on land

f = [32.8+0.425/0.425+60.8]*1200

f = [33.225/61.225]*1200

f = 651.20 Hz

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