Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point Q? (b) What is the longest wavelength for which there will be constructive interference at point Q?

Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point Q? (b) What is the longest wavelength for which there will be constructive interference at point Q?

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter24: Wave Optics

Section: Chapter Questions

Problem 7P: Two radio antennas separated by d = 3.00 102 cm. as shown in Figure P24.7, simultaneously broadcast...

See similar textbooks

Similar questions

A radio station has two antennas. The antennas are a distance d apart, where d equals half the broadcast wavelength. The antennas are driven in phase with each other. Let the x-axis be the line that runs through the two antennas. The angles are all measured counterclockwise from the +x-direction. (For the following, assume an observer is positioned a distance D far from the midpoint of the antennas, so that D ≫ d.) (a) In which directions is the strongest signal radiated? 0°, 180° 90°, 270° 0°, 90°, 180°, 270° 45°, 135°, 225°, 315° (b) In which directions is the weakest signal radiated? 0°, 180° 90°, 270° 0°, 90°, 180°, 270° 45°, 135°, 225°, 315°
Consider two identical antennas separated by 9.00 m that radiate in phase at 120 MHz. A receiver placed 150 m from both antennas measures an intensity I0. The receiver is moved so that it is 1.8 m closer to one antenna than to the other. a) What is the phase difference ϕ between the two radio waves produced by this path difference? b) In terms of I0, what is the intensity measured by the receiver at its new position?
Consider two antennas separated by 9.00 m that radiate in phase at 120 MHz. A receiver placed 150 m from both antennas measures an intensity I0. The receiver is moved so that it is 1.8 m closer to one antenna than to the other. (a) What is the phase difference ϕ between the two radio waves produced by this path difference? (b) In terms of I0, what is the intensity measured by the receiver at its new position?
A circular radar antenna on a Coast Guard ship has a diameter of 2.10 m and radiates at a frequency of 18.0 GHz. Two small boats are located 5.00 km away from the ship. How close together could the boats be and still be detected as two objects?
Two antennai (which may or may not be in phase with each other) transmit a radio wave at an AM frequency of 1500 kHz. While driving by on a semi-circular road around these antennae, you notice that there are only three totally destructive locations (one at the centerline and two at the same angle above and below the centerline as shown). What is the path length difference of the radio waves for the topmost destructive location?
Antenna B is 40.0 m to the right of antenna A. The two antennas emit electromagnetic waves that are in phase and have wavelength 7.00 m. (a) At how many points along the line connecting A and B is the interference constructive? (b) What is the smallest distance to the right of antenna A for which is there a point of constructive interference?
In an experiment to demonstrate interference, you connect two antennas to a single radio receiver. When the two antennas are adjacent to each other, the received signal is strong. You leave one antenna in place and move the other one directly away from the radio transmission tower. How far should the second antenna be moved in order to receive a minimum signal from a station that broadcasts at 103.4 MHz?
Two antennas located at points A and B are broadcasting radio waves of frequency 96.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d= 6.20 m. An observer, P, is located on the x axis, a distance x= 84.0 m from antenna A, so that APB forms a right triangle with PB as hypotenuse. What is the phase difference between the waves arriving at P from antennas A and B? A P X B 4.594x10-¹ rad Computer's answer now shown above. You are correct. Your receipt no. is 158-6031 > Previous Tries Now observer P walks along the x axis toward antenna A. What is P's distance from A when he first observes fully destructive interference between the two waves? 1.203 m As P gets closer A, the path length difference gets larger. What's the smallest path length difference that gives destructive interference? Submit Answer Tries 0/6 Submit Answer Incorrect. Tries 1/6 Previous Tries If observer P continues walking until he reaches antenna A, at how many places along the x…
It is often desirable to radiate most of the energy from a radio transmitter in particular directions rather than uniformly in all directions. Pairs or rows of antennas are often used to produce the desired radiation pattern. As an example, consider two identical vertical antennas 400 m apart, operating at 1500 kHz = 1.5 * 106 Hz (near the top end of the AM broadcast band) and oscillating in phase. At distances much greater than 400 m, in what directions is the intensity from the two antennas greatest?
When coherent electromagnetic waves with wavelength l = 120 mm are incident on a single slit of width a, the width of the central maximum on a tall screen 1.50 m from the slit is 90.0 cm. For the same slit and screen, for what wavelength of the incident waves is the width of the central maximum 180.0 cm, double the value when l = 120 mm?
A receiver located in front of a sheer cliff as shown in the figure picks up interfering signals from a nearby 265 kHz transmitter. One signal travels directly from the transmitting antenna to the receiver, and the other first travels to and bounces off the cliff. (a) What is the wavelength of the signal? λ = [ km (b) For what minimum possible distance between the cliff and the receiver will the two waves interfere constructively at the receiver? km (c) For what minimum possible distance between the cliff and the receiver will the two waves interfere destructively at the receiver? km Transmitting Cliff Receiver antenna Use c = 2.998 x 108 m/s.
The GPS (Global Positioning System) satellites are approximately 5.18 m across and transmit two low-power signals, one of which is at 1575.42 MHz (in the UHF band). In a series of laboratory tests on the satellite, you put two 1575.42 MHz UHF transmitters at opposite ends of the satellite. These broadcast in phase uniformly in all directions. You measure the intensity at points on a circle that is several hundred meters in radius and centered on the satellite. You measure angles on this circle relative to a point that lies along the centerline of the satellite (that is, the perpendicular bisector of a line which extends from one transmitter to the other). At this point on the circle, the measured intensity is 2.00 W/m². At how many other angles in the range 0° < 0 < 90° is the intensity also 2.00 W/m²? Express your answer as an integer. N = Submit Part B 0 = Submit 2 Find the four smallest (positive) angles in the range 0° < 0 < 90° for which the intensity is 2.00 W/m². Express your…