Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 27, Problem 31P
(a)
To determine
The number of diffraction minima observed in listening points in the line which is parallel to wall.
(b)
To determine
Angular directions of diffraction minima.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A steady sound with a frequency of f = 750 Hz is produced by a source located far from an open doorway set in a sound-
absorbing wall. The sound waves pass through the w = 1.18 m-wide doorway. (Assume the speed of sound is 343 m/s.)
(a) If a person walks parallel to the wall beyond the open doorway, how many diffraction minima will she encounter?
(b) What are the angular directions (in degrees) of these diffraction minima? (Enter the magnitudes from smallest to largest
starting with the first answer blank. Enter NONE in any remaining answer blanks. Do not enter any duplicate numerical
values.)
smallest
土
土
largest
Sound waves with frequency 4000 Hz and speed 350 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. The opening, which has a horizontal width of 31.0 cm, faces a wall 100 m away. Along that wall, how far from the central axis will a listener be at the first diffraction minimum and thus have difficulty hearing the sound?
The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (a) Show that the intensity drops to one-half the maximum value when sin2 a = a2/2. (b) Verify that a =1.39 rad (about 80°) is a solution to the transcendental equation of (a). (c) Show that the FWHM is u= 2 sin-1(0.443l/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00l, (e) 5.00l, and (f) 10.0l.
Chapter 27 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 27.3 - Which of the following causes the fringes in a...Ch. 27.5 - In a laboratory accident, you spill two liquids...Ch. 27.5 - Prob. 27.3QQCh. 27.6 - Prob. 27.4QQCh. 27.7 - Suppose you are observing a binary star with a...Ch. 27.8 - Ultraviolet light of wavelength 350 nm is incident...Ch. 27 - Consider a wave passing through a single slit....Ch. 27 - Prob. 2OQCh. 27 - Suppose Youngs double-slit experiment is performed...Ch. 27 - Prob. 4OQ
Ch. 27 - Prob. 5OQCh. 27 - Prob. 6OQCh. 27 - A monochromatic beam of light of wavelength 500 nm...Ch. 27 - A film of oil on a puddle in a parking lot shows a...Ch. 27 - Prob. 9OQCh. 27 - A Fraunhofer diffraction pattern is produced on a...Ch. 27 - Prob. 11OQCh. 27 - Prob. 12OQCh. 27 - Why is it advantageous to use a large-diameter...Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - Prob. 3CQCh. 27 - Prob. 4CQCh. 27 - Why is the lens on a good-quality camera coated...Ch. 27 - Prob. 6CQCh. 27 - Prob. 7CQCh. 27 - Prob. 8CQCh. 27 - A laser beam is incident at a shallow angle on a...Ch. 27 - Prob. 10CQCh. 27 - Prob. 11CQCh. 27 - Prob. 12CQCh. 27 - John William Strutt, Lord Rayleigh (1842–1919),...Ch. 27 - Prob. 1PCh. 27 - Youngs double-slit experiment underlies the...Ch. 27 - Two radio antennas separated by d = 300 m as shown...Ch. 27 - Prob. 4PCh. 27 - Prob. 5PCh. 27 - Prob. 6PCh. 27 - In Figure P27.7 (not to scale), let L = 1.20 m and...Ch. 27 - Prob. 8PCh. 27 - Prob. 9PCh. 27 - Prob. 10PCh. 27 - Two slits are separated by 0.180 mm. An...Ch. 27 - Prob. 12PCh. 27 - A pair of narrow, parallel slits separated by...Ch. 27 - Coherent light rays of wavelength strike a pair...Ch. 27 - Prob. 15PCh. 27 - Prob. 16PCh. 27 - A riverside warehouse has several small doors...Ch. 27 - Prob. 18PCh. 27 - Prob. 19PCh. 27 - Astronomers observe the chromosphere of the Sun...Ch. 27 - Prob. 21PCh. 27 - Prob. 22PCh. 27 - A beam of 580-nm light passes through two closely...Ch. 27 - Prob. 24PCh. 27 - An air wedge is formed between two glass plates...Ch. 27 - Prob. 26PCh. 27 - Prob. 27PCh. 27 - Prob. 28PCh. 27 - Prob. 29PCh. 27 - Prob. 30PCh. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - A beam of monochromatic green light is diffracted...Ch. 27 - Prob. 34PCh. 27 - Prob. 35PCh. 27 - Prob. 36PCh. 27 - Prob. 37PCh. 27 - Prob. 38PCh. 27 - Prob. 39PCh. 27 - White light is spread out into its spectral...Ch. 27 - Prob. 41PCh. 27 - Prob. 42PCh. 27 - Prob. 43PCh. 27 - Prob. 44PCh. 27 - Prob. 45PCh. 27 - Prob. 46PCh. 27 - Prob. 47PCh. 27 - Prob. 48PCh. 27 - Prob. 49PCh. 27 - Prob. 50PCh. 27 - Prob. 51PCh. 27 - A wide beam of laser light with a wavelength of...Ch. 27 - Prob. 53PCh. 27 - Prob. 54PCh. 27 - Prob. 55PCh. 27 - Prob. 56PCh. 27 - Prob. 57PCh. 27 - Prob. 58PCh. 27 - Prob. 59PCh. 27 - Prob. 60PCh. 27 - Prob. 61PCh. 27 - Prob. 62PCh. 27 - Both sides of a uniform film that has index of...Ch. 27 - Prob. 64PCh. 27 - Light of wavelength 500 nm is incident normally on...Ch. 27 - Prob. 66PCh. 27 - A beam of bright red light of wavelength 654 nm...Ch. 27 - Iridescent peacock feathers are shown in Figure...Ch. 27 - Prob. 69PCh. 27 - Prob. 70PCh. 27 - Figure CQ27.4 shows an unbroken soap film in a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Consider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?arrow_forwardA Fraunhofer diffraction pattern is produced on a screen located 1.00 m from a single slit. If a light source of wavelength 5.00 107 m is used and the distance from the center of the central bright fringe to the first dark fringe is 5.00 103 m, what is the slit width? (a) 0.010 0 mm (b) 0.100 mm (c) 0.200 mm (d) 1.00 mm (e) 0.005 00 mmarrow_forwardA beam of monochromatic green light is diffracted by a slit of width 0.550 mm. The diffraction pattern forms on a wall 2.06 m beyond the slit. The distance between the positions of zero intensity on both sides of the central bright fringe is 4.10 mm. Calculate the wavelength of the light.arrow_forward
- When a monochromatic light of wavelength 430 nm incident on a double slit of slit separation 5 m, there are 11 interference fringes in its central maximum. How many interference fringes will be in the central maximum of a light of wavelength 632.8 nm for the same double slit?arrow_forwardIn Figure P27.7 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4?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
- Sound waves with frequency 3000 Hz and speed 343 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length d = 100 m.The opening, which has a horizontal width of 30.0 cm, faces a wall 100 m away. Along that wall, how far from the central axis will a listener be at the first diffraction minimum and thus have difficulty hearing the sound? (Neglect reflections.)arrow_forwardA two-slit Young’s interference experiment is arranged with the wavelength of the light source λ = 0.5 μm. When a thin film of transparent material is put in front of one of the slits, the zero order fringe moves to the position previously occupied by the 4th order bright fringe. The index of refraction of the film is n = 1.2. Calculate the thickness of the film.arrow_forwardIn Young’s double slit experiment, red light with wavelength = 633 nm strikes a double slit where the separation between the slits is 0.580 mm. Interference fringes are formed on a screen which is placed at a distance of 1.20 m from the slits.(a) Calculate the fringe with. (b) What is the distance between the central maximum and the third dark fringe on one side of the central maximum?arrow_forward
- A 3.04-kHz tone is being produced by a speaker with a diameter of 0.207 m. The air temperature changes from 0 to 28 oC. Assuming air to be an ideal gas, find the change in the diffraction angle θ.arrow_forwardSound waves with frequency 2600 Hz and speed 343 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. The opening, which has a horizontal width of 38.7 cm, faces a wall 100 m away (the figure below). Along that wall, how far from the central axis of that wall in meters will a listener be at the first diffraction minimum and thus have difficulty hearing the sound? (Neglect reflections.)arrow_forwardThe double slit experiment is a quintessential wave experiment in physics. Given a third order fringe 5.00 cm away from the central fringe, a double slit with a separation of 0.0510 mm, and a distance between the slits and the fringes of 1.50 m, find the following. (a) wavelength 56E-9 X For a double slit, how is the distance from the central maximum to any constructive interference site (bright fringe) related to the separation of the slits, distance between the slits and the interference pattern, and the wavelength of the light? nm (b) separation between adjacent fringes cm Additional Materials Readingarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Convex and Concave Lenses; Author: Manocha Academy;https://www.youtube.com/watch?v=CJ6aB5ULqa0;License: Standard YouTube License, CC-BY