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12 Nov 2019
Two- source interference. Two identical radio antennas are located 50 m apart on a horizontal x - axis in the view from above in Figure 8.3. and are operating at the same carrier frequency f, exactly in phase with each other. A car tuned to the transmitter's carrier frequency travels along a round parallel to the y-axis, located 3,000 km the y-axis. The car stops briefly on the x-axis at position A, where the signal from the station is very strong (constructive interference is taking place). The car now moves to position B, 200 m further along the road. While travelling from A to B, the driver of the car noted that the signal gradually faded out halfway between A and B, that gradually returned to its previous strongest value when the car was at B, where again constructive interference occurs. Find the difference in the two path lengths from the antennas to point A, and write an appropriate interference condition involving an order of interference m and the wavelength lambda of the carrier waves from the antennas. (Assume the paths lie in the xy plane.) Find the difference in the two path lengths from the antennas to point B, and write an appropriate interference condition involving the same unknown order of interference m and write and the unknown wavelength lambda of the carries waves from the antennas. (Again assume the paths lie in xy plane.) Use your interference conditions of (a) and (b) to find the values of lambda and m. At what frequency f are these antennas operating?
Two- source interference. Two identical radio antennas are located 50 m apart on a horizontal x - axis in the view from above in Figure 8.3. and are operating at the same carrier frequency f, exactly in phase with each other. A car tuned to the transmitter's carrier frequency travels along a round parallel to the y-axis, located 3,000 km the y-axis. The car stops briefly on the x-axis at position A, where the signal from the station is very strong (constructive interference is taking place). The car now moves to position B, 200 m further along the road. While travelling from A to B, the driver of the car noted that the signal gradually faded out halfway between A and B, that gradually returned to its previous strongest value when the car was at B, where again constructive interference occurs. Find the difference in the two path lengths from the antennas to point A, and write an appropriate interference condition involving an order of interference m and the wavelength lambda of the carrier waves from the antennas. (Assume the paths lie in the xy plane.) Find the difference in the two path lengths from the antennas to point B, and write an appropriate interference condition involving the same unknown order of interference m and write and the unknown wavelength lambda of the carries waves from the antennas. (Again assume the paths lie in xy plane.) Use your interference conditions of (a) and (b) to find the values of lambda and m. At what frequency f are these antennas operating?