Physical Optics HW – Due Wednesday, January 12th Name:
1) Two sources emit waves that are in phase upon being emitted, and have wavelengths of 26.0 m. Do the waves interfere constructively or destructively at an observation point 78.0 m from one source and 143 m from the other source?
2) Two sources emit waves that are 180° out of phase upon being emitted, and have wavelengths l. Wave 1 travels a distance L1 and wave 2 travels a distance L2 when the two waves interfere with one another.
a) Under what conditions (relationship between L1, L2 and l) will the two waves interfere constructively?
b) Under what conditions (relationship between L1, L2 and l) will the two waves interfere destructively?
3) A person driving at 17 m/s crosses the line connecting two radio transmitters at right angles, as shown below. The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at point A, the radio picks up a maximum net signal.
What is the longest possible wavelength of the radio waves?
4) Moe, Larry and Curly stand in a line with a spacing of 1.0 m. Larry is 3.0 m in front of a pair of stereo speakers 0.8 m apart, as shown below. The speakers produce a single-frequency tone, vibrating in phase with each other. What are the two lowest frequencies that allow Larry to hear a loud tone (constructive interference) while Moe and Curly hear nothing (destructive interference)?
5) Two friends tune their radios to the same frequency and pick up a signal transmitted simultaneously by a pair of antennas. The friend who is equidistant from the antennas, at P0, receives a strong signal. The friend at point Q1 receives a very weak signal. Find the wavelength of the radio waves if d = 7.5 km, L = 14.0 km, and y = 1.88 km. Assume that Q1 is the first point of the minimum signal as one moves away from P0 in the y direction.
Solutions: 3) 300 m 4) 0.68 kHz, 2.0 kHz 5) 2 km