Concept explainers
(a)
The longest wavelength that interfere constructively.
(a)
Answer to Problem 61AP
The longest wavelength that interfere constructively is
Explanation of Solution
Write the expression to find the distance that the ray travels from the top of the transmitter to the ground.
Here,
Write the expression for the phase shift between the two waves.
Here,
Conclusion:
Substitute
Substitute
Rewrite the above equation to find the wavelength.
Substitute
Therefore, the longest wavelength that interfere constructively is
(b)
The longest wavelength that interfere destructively .
(b)
Answer to Problem 61AP
The longest wavelength that interfere destructively is
Explanation of Solution
Write the expression to find the distance that the ray travels from the top of the transmitter to the ground.
Here,
Write the expression for the phase shift between the two waves.
Here,
Conclusion:
Substitute
Substitute
Rewrite the above equation to find the wavelength.
Substitute
Therefore, the longest wavelength that interfere destructively is
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Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
- Two 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_forward35. Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d - 50.0 m and both a distance A - 35.0 m above the ground. The receiver can receive sig- nals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume the ground is level between the transmitter and receiver and a 180° phase shift occurs upon reflection. Determine the longest wave- lengths that interfere (a) constructively and (b) destructively. Transmitter Recriver Figure P36.35 Problems 35 and 36.arrow_forwardTwo 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…arrow_forward
- Two 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_forwardAn engineer, investigating the behavior of radio waves, builds a box 7.20 m long. Inside the box at one end is a small radio transmitter that emits radiation with a wavelength of 0.120 m. A receiver is placed at the other end, 7.20 m away. Assume both the transmitter and the receiver are on the floor of the box. The walls and floor of the box interior are treated to minimize reflection of radio waves. The ceiling of the box interior, however, is metal, so the radio waves can reflect off of it almost perfectly. The radio waves can take two paths from the transmitter to the receiver: a straight-line path, and a path that reflects off the ceiling of the box interior. Note that there is a phase shift when the waves reflect off the ceiling. (a) What is the minimum (nonzero) height of the box ceiling (in m) that could produce destructive interference between the direct and reflected waves at the receiver's location? (b) What If? Some modern Wi-Fi antennas emit frequencies in the 5 GHz band.…arrow_forwardThe figure below shows a radio-wave transmitter and a receiver, both h = 49.0 m above the ground and d = 510 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 A/2 phase shift occurs upon reflection, determinė the longest wavelengths that interfere destructively.arrow_forward
- Astronomers observe a 60.0 MHz radio source both directly and by reflection from the sea as shown in Figure P37.7. If the receiving dish is 20.0 m above sea level, what is the angle of the radio source above the horizon at the first maximum?arrow_forwardA thin layer of oil with index of refraction no = 1.47 is floating above the water. The index of refraction of water is nw = 1.3. The index of refraction of air is na = 1. A light with wavelength λ = 325 nm goes in from the air to oil and water. Part (a) Express the wavelength of the light in the oil, λo, in terms of λ and no. Part (b) Express the minimum thickness of the film that will result in destructive interference, tmin, in terms of λo. Part (c) Express tmin in terms of λ and no. Part (d) Solve for the numerical value of tmin in nm.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
- Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a slit 12.0 cm wide. A microphone is placed 8.00 m directly in front of the center of the slit, corresponding to point O in Fig. The microphone is then moved in a direction perpendicular to the line from the center of the slit to point O. At what distances from O will the intensity detected by the microphone be zero?arrow_forwardA flat piece of glass is held stationary and horizontal above the highly polished, flat top end of a 8.50-cm-long vertical metal rod that has its lower end rigidly fixed. The thin film of air between the rod and glass is observed to be bright by reflected light when it is illuminated by light of wavelength 530 nm. As the temperature is slowly increased by 21.5°C, the film changes from bright to dark and back to bright 200 times. What is the coefficient of linear expansion of the metal? °c-1arrow_forwardIn a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0 ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light 21.2 ns to travel from the laser to the photocell. What is the wavelength of the light in the glass?arrow_forward
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning