The figure below shows a radio-wave transmitter and a receiver, both h = 57.0 m above the ground and d = 670 m apart. The receiver can receive signals directly from the transmitter and indirectly from signals that bounce off the ground. Transmitter Receiver (a) If the ground is level between the transmitter and receiver and a 1/2 phase shift occurs upon reflection, determine the longest wavelengths that interfere constructively. (b) If the ground is level between the transmitter and receiver and a 1/2 phase shift occurs upon reflection, determine the longest wavelengths that interfere destructively.

The figure below shows a radio-wave transmitter and a receiver, both h = 57.0 m above the ground and d = 670 m apart. The receiver can receive signals directly from the transmitter and indirectly from signals that bounce off the ground. Transmitter Receiver (a) If the ground is level between the transmitter and receiver and a 1/2 phase shift occurs upon reflection, determine the longest wavelengths that interfere constructively. (b) If the ground is level between the transmitter and receiver and a 1/2 phase shift occurs upon reflection, determine the longest wavelengths that interfere destructively.

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 69AP: Figure P24.69 shows a radio-wave transmitter and a receiver, both h = 50.0 m above the ground and d...

See similar textbooks

Similar questions

The movable mirror of a Michelson interferometer is attached to one end of a thin metal rod of length 23.3 mm. The other end of the rod is anchored so it does not move. As the temperature of the rod changes from 15°C to 25 C , a change of 14 fringes is observed. The light source is a He Ne laser, =632.8 nm . What is the change in length of the metal bar, and what is its thermal expansion coefficient?
Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.
To save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers. (a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observed at λ1, where λ1 > λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in Equations 27.13 and 27.14 in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film.
As a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let = 0.626 and d0 = 4.00 . Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure. Figure P3.38 Atomic planes in a cubic lattice.
A beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure P27.23. For what minimum nonzero value of the plate separation d is the transmitted light bright?
Two radio antennas separated by d = 3.00 102 cm. as shown in Figure P24.7, simultaneously broadcast identical signals at the same the signals. (a) If the car is at the position of the second maximum wavelength. A car travels due north along a straight line at position x = 1.00 103 m from the center point between the antennas and its radio receives the signal. (a) If the car is at the position of the second maximum after that at point O when it has traveled a distance of y = 4.00 102 m northward, what is the wavelength of the signals? (b) How much farther must the car travel from thus position to encounter the next minimum in reception? Hint: Do not use the small-angle approximation in this problem.
How many helium atoms, each with a radius of about 31 pm, must be placed end to end to have a length equal to one wavelength of 470 nm blue light?
A beam of light with wavelength of 1.00 µm and M2 = 20 is incident on an aperture of 1.5 mm diameter. a) Calculate the divergence angle of the beam in degrees (give the cone full-angle). b) Calculate the diameter of the beam at a distance of 10.00 m away from the aperture in the propagation direction in units of cm. c) It is given that the longitudinal (temporal) coherence length is 70 times the transverse (spatial) coherence length. Calculate the wavelength linewidth of the light in units of pm.a
Two radio antennas are separated by 1.60 m. Both broadcast identical 750 MHz waves. If you walk around the antennas in a circle of radius 10.0 m, how many maxima will you detect?
The central bright fringe in a single-slit diffraction pattern has a width that equals the distance between the screen and the slit. Find the ratio A/W of the wavelength A of the light to the width W of the slit. Number i eTextbook and Media Units < J 16.
Parameters of a Dielectric Waveguide. Light of free-space wavelength X, = 0.87 um is guided by a thin planar film of width d = 2 μm and refractive index n₁ = 1.6 surrounded by a medium of refractive index n₂ = 1.4. (a) Determine the critical angle 0, and its complement c, the numerical aperture NA, and the maximum acceptance angle for light originating in air (n = 1). (b) Determine the number of TE modes. (c) Determine the bounce angle and the group velocity v of the m= 0 TE mode.