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

Question

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 7.5 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:

Explanation / Answer

Frequency,f=7.5 MHz

speed,v=15 km/hr

We know that the equation is ,n . wavelength = x . d / L

where,

L = distance of ship from shore ( 2 . 105 m )

d = separation of sources ( 104 m )

x = Distance between the maximum amplitudes

n = 1

wavelength = 3 * 108 / 7.5*106=40 m

So,x=L*wavelength/d=2*105*40/104= 800m

Then the time you want is t=x / v=800/15 km* km/(1000m)hr=0.0533*60 min=3.2 min

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