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 = 74.5 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 v current = 15.0 km/h. The trailing ship transmits a sonar signal at a frequency of 1200.0 Hz through the water. What frequency is monitored by the leading ship? (Use 1533 m/s as the speed of sound in ocean water. Express your answer to five significant figures.)

Explanation / Answer

in the reference frame of the leading ship, the trailing ship is approaching at 29.5km/h or 8.19m/s

the frequency observed by the leading ship will be

f(obs) = c/(c-v) x f(rest)

where c is the speed of sound, v the relative velocities of the ships, and f (rest) the frequency as measured in the rest frame of the emitting ship

we have

f(obs) = 1533/(1533-8.19) x 1200Hz

f(obs) = 1206.44Hz = Ans

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