(Solved) Two radio antennas are 10 km apart on a north-south axis on a seacoast. The ante

mikael

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10 years ago

Two radio antennas are 10 km apart on a north-south axis on a seacoast. The ante

Two radio antennas are 10 km apart on a north-south axis on a seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 7.50 MHz. A steamship, 200 km offshore, travels due north at a speed of 15 km/hr and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. The time interval until the next occurrence of maximum reception is closest to:
A) 3.2 min
B) 2.4 min
C) 4.0 min
D) 4.8 min
E) 5.6 min

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cmt0730

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2 years ago

Two radio antennas are 10 km apart on a north-south axis on a seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 4.70 MHz. A steamship, 200 km offshore, travels due north at a speed of 15 km/hr and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. What is the time interval until the next occurrence of maximum reception?

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meggsnbacon

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2 years ago

Quote from: cmt0730 (2 years ago)

wavelength = c / f = 3x10^8 / 0.047x10^8 = 63.83 m = 0.06383 km

Treat this problem as a double-slit interference problem. Assume the steamship is at the central maximum initially. Find the distance to the next maximum, i.e. m = 1.

Then...

m * wavelength = d sin@

Since @ is "small", sin@ = y/L and

m * wavelength = d y / L

y = L m wavelength / d = 200 * 1 * 0.06383 / 10 = 1.2766 km

time = distance / speed = 1.2766 km / 15 km/hr = 0.0851 hr = 5.106 minutes

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