An Introduction to Physical Science
14th Edition
ISBN: 9781305079137
Author: James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher: Cengage Learning
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Chapter 7, Problem 12MC
To determine
The condition in which the total constructive interference occur.
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Two in-phase sources of waves are separated by a distance of 4.00 m.These sources produce identical waves that have a wavelength of 5.00 m.On the line between them, there are two places at which the same type ofinterference occurs. (a) Is it constructive or destructive interference, and(b) where are the places located?
(Figure 1) shows the circular wave fronts emitted by two wave sources.
Are these sources in phase or out of phase?
Make a table with rows labeled P, Q, and R and columns labeled r1, r2, Δr, and C/D. Fill in the table for points P, Q, and R, giving the distances as multiples of λ and indicating, with a C or a D, whether the interference at that point is constructive or destructive.
Two interfering light waves have intensities of 20\,W\,m−2 and 40\,W\,m−2, and the phase difference between them at some point P is π/3. The intensity at P, in W m−2−2, including interference is:(give your answer as a decimal to 1 d.p. )
Chapter 7 Solutions
An Introduction to Physical Science
Ch. 7.1 - Prob. 1PQCh. 7.1 - Prob. 2PQCh. 7.2 - What causes light refraction, and what does the...Ch. 7.2 - Prob. 2PQCh. 7.2 - Prob. 7.1CECh. 7.3 - What are the shapes of converging and diverging...Ch. 7.3 - Prob. 2PQCh. 7.3 - Prob. 7.2CECh. 7.4 - Prob. 1PQCh. 7.4 - Prob. 2PQ
Ch. 7.4 - Prob. 7.3CECh. 7.5 - Prob. 1PQCh. 7.5 - Prob. 2PQCh. 7.6 - Prob. 1PQCh. 7.6 - Prob. 2PQCh. 7 - KEY TERMS 1. reflection (7.1) 2. ray 3. law of...Ch. 7 - KEY TERMS 1. reflection (7.1) 2. ray 3. law of...Ch. 7 - Prob. CMCh. 7 - Prob. DMCh. 7 - Prob. EMCh. 7 - Prob. FMCh. 7 - Prob. GMCh. 7 - KEY TERMS 1. reflection (7.1) 2. ray 3. law of...Ch. 7 - Prob. IMCh. 7 - Prob. JMCh. 7 - Prob. KMCh. 7 - Prob. LMCh. 7 - Prob. MMCh. 7 - Prob. NMCh. 7 - Prob. OMCh. 7 - Prob. PMCh. 7 - Prob. QMCh. 7 - Prob. RMCh. 7 - Prob. SMCh. 7 - Prob. TMCh. 7 - Prob. UMCh. 7 - Prob. VMCh. 7 - For ray reflections from a surface, which...Ch. 7 - To what does the law of reflection apply? (a)...Ch. 7 - What is the case when the angle of refraction is...Ch. 7 - In refraction, which of the following wave...Ch. 7 - A plane mirror _____. (7.3) (a) produces both real...Ch. 7 - Prob. 6MCCh. 7 - Prob. 7MCCh. 7 - Which of the following is true of a concave lens?...Ch. 7 - Which is true of a virtual image? (7.4) (a) It is...Ch. 7 - Prob. 10MCCh. 7 - Which is true of diffraction? (7.6) (a) It occurs...Ch. 7 - Prob. 12MCCh. 7 - Prob. 1FIBCh. 7 - Prob. 2FIBCh. 7 - Prob. 3FIBCh. 7 - Prob. 4FIBCh. 7 - Prob. 5FIBCh. 7 - Prob. 6FIBCh. 7 - Prob. 7FIBCh. 7 - Prob. 8FIBCh. 7 - A virtual image is always formed by a(n) ___ lens....Ch. 7 - Prob. 10FIBCh. 7 - Prob. 11FIBCh. 7 - Prob. 12FIBCh. 7 - For specular reflection, what is the situation...Ch. 7 - Dutch painter Vincent van Gogh was emotionally...Ch. 7 - When you walk toward a full-length plane mirror,...Ch. 7 - How long does the image of a 12-in. ruler appear...Ch. 7 - Where would an observer see the image of the arrow...Ch. 7 - Prob. 6SACh. 7 - Prob. 7SACh. 7 - Prob. 8SACh. 7 - Prob. 9SACh. 7 - Prob. 10SACh. 7 - Prob. 11SACh. 7 - What relationships exist between the center of...Ch. 7 - Prob. 13SACh. 7 - Prob. 14SACh. 7 - What happens to a light ray that passes through...Ch. 7 - Prob. 16SACh. 7 - Prob. 17SACh. 7 - Prob. 18SACh. 7 - Where is a diverging lens thickest?Ch. 7 - Prob. 20SACh. 7 - Why are slides put into a slide projector upside...Ch. 7 - Prob. 22SACh. 7 - Prob. 23SACh. 7 - Prob. 24SACh. 7 - Prob. 25SACh. 7 - Prob. 26SACh. 7 - While you are looking through two polarizing...Ch. 7 - Prob. 28SACh. 7 - Why do sound waves bend around everyday objects,...Ch. 7 - Prob. 30SACh. 7 - Prob. 31SACh. 7 - Prob. 32SACh. 7 - Prob. 1VCCh. 7 - Prob. 1AYKCh. 7 - When you look at a window from the inside at...Ch. 7 - Prob. 3AYKCh. 7 - Prob. 4AYKCh. 7 - How would a fish see the above-water world when...Ch. 7 - Light is incident on a plane mirror at an angle of...Ch. 7 - Light is incident on a plane mirror at an angle of...Ch. 7 - Prob. 3ECh. 7 - How much longer must the minimum length of a plane...Ch. 7 - Prob. 5ECh. 7 - The speed of light in a particular type of glass...Ch. 7 - What percentage of the speed of light in vacuum is...Ch. 7 - The speed of light in a certain transparent...Ch. 7 - Prob. 9ECh. 7 - Sketch ray diagrams for a concave mirror showing...Ch. 7 - An object is placed 15 cm from a convex spherical...Ch. 7 - A reflecting, spherical Christmas tree ornament...Ch. 7 - Prob. 13ECh. 7 - Sketch ray diagrams for a spherical convex lens...Ch. 7 - An object is placed 45 cm in front of a converging...Ch. 7 - An object is placed in front of a converging lens...Ch. 7 - Prob. 17ECh. 7 - Prob. 18E
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- If two objects are placed together and neither one undergoes any change, they have the same …………………. If the critical angle for total internal reflection inside a certain transparent material is found to be 48.00, calculate the index of refraction of the material. The speed of a sound wave in air depends only on ……………. Light bends on entering glass from air because its ……...is less in the glass.arrow_forwardAssume the indices of refraction for air, water, and glass are 1.00, 1.33, and 1.50, respectively. When illuminated from above, a ray reflected from the air-water interface undergoes a phase shift of φ 1 = π, and a ray reflected at the water-glass interface also undergoes a phase shift of π. Thus, the two rays are unshifted in phase relative to each other due to reflection. For constructive interference, the path difference 2t must equal an integer number (m) of wavelengths in water. a. Derive the equation in terms of λ based on the situation above. b. If this m-value is an integer the wavelength undergoes constructive interference upon reflection in terms of λ, compute for the wavelengths for the following thickness: t= 2 x 10 5 m at m 700 nm and m 400 nmarrow_forwardDiscuss the difference in the interference patterns produced by minimum and maximum amplitude. Discuss the difference in the interference patterns produced by minimum and maximum separation of wave sources.arrow_forward
- A room contains air in which the speed of sound is 343 m/s.The walls of the room are made of concrete, in which thespeed of sound is 1 850 m/s. (a) Find the critical angle fortotal internal reflection of sound at the concrete–air boundary.(b) In which medium must the sound be traveling inorder to undergo total internal reflection? (c) “A bare concretewall is a highly efficient mirror for sound.” Give evidencefor or against this statement.arrow_forwardTwo 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_forwardThe coherence length of a wavetrain is the distance over which the phase constant is the same. (a) If an individual atom emits coherent light for 1x10-8 seconds, what is the coherence length of the wavetrain? (b) Suppose a partially reflecting mirror separates this wave train into two parts that are later reunited after one beam travels 5m and the other travels 10m. Do the waves produce interference fringes observable by a human eye?arrow_forward
- Waves from a radio station have a wavelength of 250 m. They travel by two paths to a home receiver 20.0 km from the transmitter. One path is a direct path, and the second is by reflection from a mountain directly behind the home receiver. What is the minimum distance from the mountain to the receiver that produces destructive interference at the receiver? (Assume that no phase change occurs on reflection from the mountain.)arrow_forward1)) Electromagnetic radiation of intensity I0 = 380 W/m^2 passes through two parallel. Arrow slots that are d = 2.8 μm part and strikes a screen located L = 1.4 m from the slits. The intensity of the radiation in the screen at y = 4.6 mm from the central interference maximum is I = 55 W/m^2. A)) Calculate the phase difference, in radians, between the rays from the two slits as they strike the screen at the specified distance from the center maximum, B)) Calculate the average wavelength of the radiation, in nanometers.arrow_forwardIn a certain crystal the spacing between crystal planes is 0.165 nm. (a) If you shine a beam of x rays of wavelength 0.124 nm on this crystal, for what angle between the beam and the crystal planes does the first strong interference maximum occur? (b) For what larger angles (if any) do strong interference maxima occur?arrow_forward
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