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Two independent radio towers (which may or may not be in phase with each other) transmit radio waves with a frequency of 3,000 kHz. The towers transmit these waves to two islands (Ogakor and Kucha), which always receive a constant constructive interference signal. Both of the islands are located at angle B with respect to the centerline (but on opposite sides of the centerline). Ogakor Island is 11,858 meters from Tower B and 11,508 meters from Tower A. Kucha Island is 12,512 meters from Tower A and 12,162 meters from Tower B. The distance, d, between the two towers is unknown but it is much less than the distances given above.

Two independent radio towers (which may or may not be in phase with each other) transmit radio waves with a frequency of 3,000 kHz. The towers transmit these waves to two islands (Ogakor and Kucha), which always receive a constant constructive interference signal. Both of the islands are located at angle B with respect to the centerline (but on opposite sides of the centerline). Ogakor Island is 11,858 meters from Tower B and 11,508 meters from Tower A. Kucha Island is 12,512 meters from Tower A and 12,162 meters from Tower B. The distance, d, between the two towers is unknown but it is much less than the distances given above.

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c. Since Ogakor Island experiences constructive interference with the path length difference found in part b), what must be Aø (the constant phase difference) between Tower A and Tower B (more than one answer may be correct)? d. What type of interference must occur at the centerline (i.e. constructive, destructive, or neither) based upon on your answers to parts b) and c)? Note that there is zero path length difference between light from Tower A and Tower B on the centerline. e. What is the path length difference for radio waves travelling from Tower A to Kucha Island compared to radio waves traveling from Tower B to Kucha Island? What is the total phase difference for waves travelling from Tower B compared to Tower A? f. A boat goes in a straight line from Ogakor Island to Kucha Island as shown in the diagram above. How many minima (i.e. completely destructive lines) will the boat detect as it goes from Ogakor Island to Kucha Island?
Transcribed Image Text:c. Since Ogakor Island experiences constructive interference with the path length difference found in part b), what must be Aø (the constant phase difference) between Tower A and Tower B (more than one answer may be correct)? d. What type of interference must occur at the centerline (i.e. constructive, destructive, or neither) based upon on your answers to parts b) and c)? Note that there is zero path length difference between light from Tower A and Tower B on the centerline. e. What is the path length difference for radio waves travelling from Tower A to Kucha Island compared to radio waves traveling from Tower B to Kucha Island? What is the total phase difference for waves travelling from Tower B compared to Tower A? f. A boat goes in a straight line from Ogakor Island to Kucha Island as shown in the diagram above. How many minima (i.e. completely destructive lines) will the boat detect as it goes from Ogakor Island to Kucha Island?
Two independent radio towers (which may or may not be in phase with each other) transmit radio waves with a frequency of 3,000 kHz. The towers transmit these waves to two islands (Ogakor and Kucha), which always receive a constant constructive interference signal. Both of the islands are located at angle ß with respect to the centerline (but on opposite sides of the centerline). centerline --> Kucha Island Ogakor Island boat course Ogakor Island is 11,858 meters from Tower B and 11,508 meters from Tower A. Kucha Island is 12,512 meters from Tower A and 12,162 meters from Tower B. The distance, d, between the two towers is unknown but it is much less than the distances given above. Tower A Tower B d = ? What is the wavelength for these transmitted radio waves? а. b. What is the path length difference for radio waves travelling from Tower A to Ogakor Island compared to radio waves traveling from Tower B to Ogakor Island? Is this path length difference an integer number of the wavelength? Is this path length difference a half-integer number of the wavelength?
Transcribed Image Text:Two independent radio towers (which may or may not be in phase with each other) transmit radio waves with a frequency of 3,000 kHz. The towers transmit these waves to two islands (Ogakor and Kucha), which always receive a constant constructive interference signal. Both of the islands are located at angle ß with respect to the centerline (but on opposite sides of the centerline). centerline --> Kucha Island Ogakor Island boat course Ogakor Island is 11,858 meters from Tower B and 11,508 meters from Tower A. Kucha Island is 12,512 meters from Tower A and 12,162 meters from Tower B. The distance, d, between the two towers is unknown but it is much less than the distances given above. Tower A Tower B d = ? What is the wavelength for these transmitted radio waves? а. b. What is the path length difference for radio waves travelling from Tower A to Ogakor Island compared to radio waves traveling from Tower B to Ogakor Island? Is this path length difference an integer number of the wavelength? Is this path length difference a half-integer number of the wavelength?
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