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A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that
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- 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°arrow_forwardTwo antennas located at points A and B are broadcasting radio waves of frequency 104.0 MHz. The signals start in phase with each other. The two antennas are separated by a distance d = 8.7 m. An observer is located at point P on the x axis, a distance x = 110.0 m from antenna A. The points A, P, and B form a right triangle. Now observer P walks along the x axis toward antenna A. What is P's distance from A when they first observe fully constructive interference between the two waves?arrow_forwardTwo sources are emitting coherent, monochromatic EM waves with a wavelength of 2 cm in air. Source 1 is embedded in a material with index of refraction n1 = 1.5. The distance between source 1 and the edge of the material is 6 cm. You can assume nair = 1. At the point marked with an X, which is 9 cm from source 2 and 3 cm from the edge of the material that source 1 is embedded inside, what kind of interference will you find between EM waves from the two sources? Group of answer choices Destructive Constructivearrow_forward
- Coherent electromagnetic waves with wavelength λ = 500 nm pass through two identical slits. The width of each slit is a, and the distance between the centers of the slits is d = 9.00 mm. (a) What is the smallest possible width a of the slits if the m = 3 maximum in the interference pattern is not present? (b) What is the next larger value of the slit width for which the m = 3 maximum is absent?arrow_forwardTwo antennas located at points A and B are broadcasting radio waves of frequency 104.0 MHz. The signals start in phase with each other. The two antennas are separated by a distance d = 8.7 m. An observer is located at point P on the x axis, a distance x = 110.0 m from antenna A. The points A, P, and B form a right triangle. What is the phase difference between the waves arriving at P from antennas A and B? Enter your answer in radiansarrow_forwardThe ship in the figure below travels along a straight line parallel to the shore and a distance d = 560 m from it. The ship's radio receives simultaneous signals of the same frequency from antennas A and B, separated by a distance L = 840 m apart. The signals interfere constructively at point C, which is equidistant from A and B. The signal goes through the first minimum at point D, which is directly outward from the shore from point B. Determine the wavelength of the radio waves.arrow_forward
- Short-wave radio antennas A and B are connected to the same transmitter and emit coherent waves in phase and with the same frequency f. You must determine the value of f and the placement of the antennas that produce a maximum intensity through constructive interference at a receiving antenna that is located at point P, which is at the corner of your garage. First you place antenna A at a point 240.0 m due east of P. Next you place antenna B on the line that connects A and P, a distance x due east of P, where x < 240.0 m. Then you measure that a maximum in the total intensity from the two antennas occurs when x = 210.0 m, 216.0 m, and 222.0 m. You don’t investigate smaller or larger values of x. (Treat the antennas as point sources.) (a) What is the frequency f of the waves that are emitted by the antennas? (b) What is the greatest value of x, with x < 240.0 m, for which the interference at P is destructive?arrow_forwardA 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.arrow_forwardThe next two questions pertain to the same situation. Two antennas located at points A and B are broadcasting radio waves of a certain wavelength λ, perfectly in phase with each other. The two antennas are separated by a distance d = 300 m. An observer is at point P, located on the x-axis, at a distance x=400 m from antenna A, so that APB forms a right triangle with PB as hypotenuse. Another observer is at point Q, located on the y-axis, at a distance y=200 m from A. A d = 300m B x=400 m y y= = 200 m P X 7) For which one of the following wavelength values will the observer at point P detect a maximum signal strength? A) λ = 60 m B) λ = 80 m C) λ = 100 m |D) λ = 120 m E) λ = 140 m 8) If the wavelength of the radio waves used is λ = 50 m, the observer at point Q will see a A) constructive interference B) destructive interference The next two questions pertain to the situation described below.arrow_forward
- Two radio antennas are 120 m apart on a north-south line, and they radiate in phase at a frequency of 3.4 MHz. All radio measurements are made far from the antennas. If the east-west reference line passes midway between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructive interference of two radio waves occurs?arrow_forwardA beam of light with wavelength 440 nm in air hits a thin piece of glass 10.28 microns thick (with refractive index 1.55) at an angle of 40.8 degrees to the normal. What is the path difference between the two reflections from the layers of the glass, in wavelengths? [Note to get the phase shift we multiply this number by 2π, but this is modulo 2π, i.e. any integer number of wavelengths are 2π phase shifts, equivalent to no phase shift... basically in terms of phase we only really need the non-integer part of your answer. Note also that for the phase shift we would need to add a π for the reflection off the glass-air interface.]arrow_forwardTwo light sources can be adjusted to emit monochromatic light of any visible wavelength. The two sources are coherent, 2.04 mm apart, and in line with an observer, so that one source is 2.04 mm farther from the observer than the other. (a) For what visible wavelengths (380 to 750 nm) will the observer see the brightest light, owing to constructive interference? (b) How would your answers to part (a) be affected if the two sources were not in line with the observer, but were still arranged so that one source is 2.04 mm farther away from the observer than the other? (c) For what visible wavelengths will there be destructive interference at the location of the observer?arrow_forward
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