Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 16, Problem 38P
Two sinusoidal waves of the same frequency are to be sent in the same direction along a taut string. One wave has an amplitude of 5.0 mm. the other 8.0 mm. (a) What phase difference ϕ1 between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude? (c) What phase difference ϕ2 results in the largest amplitude of the resultant wave? (d) What is that largest amplitude? (e) What is the resultant amplitude if the phase angle is (ϕ1 − ϕ2)/2?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Two sinusoidal waves of the same frequency are to be sent in the same direction along a taut string. One wave has an amplitude of 5.0 mm, the other 8.0 mm. (a) What phase difference f1 between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude? (c) What phase difference f2 results in the largest amplitude of the resultant wave? (d) What is that largest amplitude? (e) What is the resultant amplitude if the phase angle is (f1 - f2)/2?
These two waves travel along the same string:
Y1 = (3.79 mm) sin(1.75TX - 440tt)
Y2 = (5.82 mm) sin(1.75TX - 440at + 0.8617rad).
What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.14 mm is also to be sent along the string in the same direction as the first two
waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave?
(a) Number
4.29247
Units
mm
(b) NumberTT1.4264
Units
rad
(c) Number To.708
Units
rad
Two travelling sinusoidal waves are described by the wave function
y1 = 5.00 sin [π (4.00x = 1 200t)] ,
y2 = 5.00 sin [π (4.00x – 1 200t - 0.250)]
where x, y1, and y2 are in meters and t is in seconds.
(a) what is the amplitude of the resultant wave function y1 + y2?
(b) what is the frequency of the resultant wave function?
Chapter 16 Solutions
Fundamentals of Physics Extended
Ch. 16 - Prob. 1QCh. 16 - Prob. 2QCh. 16 - Prob. 3QCh. 16 - Prob. 4QCh. 16 - Prob. 5QCh. 16 - The amplitudes and phase differences for four...Ch. 16 - Prob. 7QCh. 16 - a If a standing wave on a siring is given by y't =...Ch. 16 - Prob. 9QCh. 16 - If you set up the seventh harmonic on a string, a...
Ch. 16 - Prob. 11QCh. 16 - If a wave yx, t = 6.0mm sinkx 600 rad/st ...Ch. 16 - Prob. 2PCh. 16 - A wave has an angular frequency of 110 rad/s and a...Ch. 16 - Prob. 4PCh. 16 - A sinusoidal wave travels along a string. The time...Ch. 16 - Prob. 6PCh. 16 - A transverse sinusoidal wave is moving along a...Ch. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 11PCh. 16 - GO The function yx, t = 15.0 cm cosx 15 t, with x...Ch. 16 - Prob. 13PCh. 16 - The equation of a transverse wave on a string is y...Ch. 16 - Prob. 15PCh. 16 - The speed of a transverse wave on a string is 170...Ch. 16 - The linear density of a string is 1.6 104 kg/m. A...Ch. 16 - Prob. 18PCh. 16 - SSM What is the speed of a transverse wave in a...Ch. 16 - The tension in a wire clamped at both ends is...Ch. 16 - ILW A 100 g wire is held under a tension of 250 N...Ch. 16 - A sinusoidal wave is traveling on a string with...Ch. 16 - SSM ILW A sinusoidal transverse wave is traveling...Ch. 16 - Prob. 24PCh. 16 - A uniform rope of mass m and length L hangs from a...Ch. 16 - A string along which waves can travel is 2.70 m...Ch. 16 - Prob. 27PCh. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Use the wave equation to find the speed of a wave...Ch. 16 - Prob. 31PCh. 16 - What phase difference between two identical...Ch. 16 - Prob. 33PCh. 16 - Prob. 34PCh. 16 - SSM Two sinusoidal waves of the same frequency...Ch. 16 - Four waves are to be sent along the same string,...Ch. 16 - GO These two waves travel along the same string:...Ch. 16 - Two sinusoidal waves of the same frequency are to...Ch. 16 - Two sinusoidal waves of the same period, with...Ch. 16 - Two sinusoidal waves with identical wavelengths...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - SSM WWW What are a the lowest frequency, b the...Ch. 16 - A 125 cm length of string has mass 2.00 g and...Ch. 16 - Prob. 45PCh. 16 - String A is stretched between two clamps separated...Ch. 16 - Prob. 47PCh. 16 - If a transmission line in a cold climate collects...Ch. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - A rope, under a tension of 200 N and fixed at both...Ch. 16 - Prob. 53PCh. 16 - Prob. 54PCh. 16 - GO The following two waves are sent in opposite...Ch. 16 - A standing wave pattern on a string is described...Ch. 16 - A generator at one end of a very long string...Ch. 16 - GO In Fig. 16-42, a string, tied to a sinusoidal...Ch. 16 - GO In Fig. 16-43, an aluminum wire, of length L1 =...Ch. 16 - Prob. 60PCh. 16 - Prob. 61PCh. 16 - Prob. 62PCh. 16 - A wave has a speed of 240 m/s and a wavelength of...Ch. 16 - The equation of a transverse wave traveling alone...Ch. 16 - The equation of a transverse wave traveling along...Ch. 16 - Prob. 66PCh. 16 - Prob. 67PCh. 16 - Prob. 68PCh. 16 - Prob. 69PCh. 16 - Prob. 70PCh. 16 - A transverse sinusoidal wave is generated at one...Ch. 16 - Prob. 72PCh. 16 - Prob. 73PCh. 16 - Prob. 74PCh. 16 - a What is the fastest transverse wave that can be...Ch. 16 - A standing wave results from the sum of two...Ch. 16 - Prob. 77PCh. 16 - Prob. 78PCh. 16 - Prob. 79PCh. 16 - When played in a certain manner, the lowest...Ch. 16 - A sinusoidal transverse wave traveling in the...Ch. 16 - Two sinusoidal waves of the same wavelength travel...Ch. 16 - Prob. 83PCh. 16 - Prob. 84PCh. 16 - Prob. 85PCh. 16 - a Write an equation describing a sinusoidal...Ch. 16 - A wave on a string is described by yx, t = 15.0...Ch. 16 - Prob. 88PCh. 16 - Two waves are described by...Ch. 16 - Prob. 90PCh. 16 - SSM In a demonstration, a 1.2 kg horizontal rope...Ch. 16 - Prob. 92PCh. 16 - A traveling wave on a string is described by...Ch. 16 - Prob. 94PCh. 16 - Prob. 95PCh. 16 - Consider a loop in the standing wave created by...
Additional Science Textbook Solutions
Find more solutions based on key concepts
15.1 What purpose do the bla and lacZ genes serve in the plasmid vector ?
Genetic Analysis: An Integrated Approach (3rd Edition)
WHAT IF? You are studying nitrogen cycling on the Serengeti Plain in Africa. During your experiment, a herd of ...
Campbell Biology in Focus (2nd Edition)
What are four functions of connective tissue?
Anatomy & Physiology (6th Edition)
18. SCIENTIFIC THINKING By measuring the fossil remains of Homo floresiensis, scientists have estimated its wei...
Campbell Biology: Concepts & Connections (9th Edition)
Which types of muscular tissue have gap junctions?
Principles of Anatomy and Physiology
Fibrous connective tissue consists of ground substance and fibers that provide strength, support, and flexibili...
Human Biology: Concepts and Current Issues (8th Edition)
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
- Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)arrow_forwardA string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and a sinusoidal wave with an amplitude of 2.00 cm is induced on the string, what must the frequency be for an average power of 100.00 W?arrow_forwardA taut rope has a mass of 0.180 kg and a length of 3.60 m. What power must be supplied to the rope so as to generate sinusoidal waves having an amplitude of 0.100 m and a wavelength of 0.500 m and traveling with a speed of 30.0 m/s?arrow_forward
- The equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?arrow_forwardA harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all values are in the appropriate SI units. a. What are the propagation speed and direction of the waves travel? b. What are the waves period and wavelength? c. What is the amplitude? d. If the amplitude is doubled, what happens to the speed of the wave?arrow_forwardWhen a standing wave is set up on a string fixed at both ends, which of the following statements is true? (a) The number of nodes is equal to the number of antinodes. (b) The wavelength is equal to the length of the string divided by an integer. (c) The frequency is equal to the number of nodes times the fundamental frequency. (d) The shape of the string at any instant shows a symmetry about the midpoint of the string.arrow_forward
- Rank the waves represented by the following functions from the largest to the smallest according to (i) their amplitudes, (ii) their wavelengths, (iii) their frequencies, (iv) their periods, and (v) their speeds. If the values of a quantity are equal for two waves, show them as having equal rank. For all functions, x and y are in meters and t is in seconds. (a) y = 4 sin (3x 15t) (b) y = 6 cos (3x + 15t 2) (c) y = 8 sin (2x + 15t) (d) y = 8 cos (4x + 20t) (e) y = 7 sin (6x + 24t)arrow_forwardA steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires?arrow_forwardThe amplitude of a wave is doubled, with no other changes made to the wave. As a result of this doubling, which of the following statements is correct? (a) The speed of the wave changes. (b) The frequency of the wave changes. (c) The maximum transverse speed of an element of the medium changes. (d) Statements (a) through (c) are all true. (e) None of statements (a) through (c) is true.arrow_forward
- Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes of 6.00 cm, a wavelength of 4.3 m, and a period of 6.00 s, but one has a phase shift of an angle =0.50 rad. What is the height of the resultant wave at a time t=3.15 s and a position x=0.45 m ?arrow_forwardA sound wave can be characterized as (a) a transverse wave, (b) a longitudinal wave, (c) a transverse wave or a longitudinal wave, depending on the nature of its source, (d) one that carries no energy, or (e) a wave that does not require a medium to be transmitted from one place to the other.arrow_forwardAssume two identical sinusoidal waves are moving through the same medium in the same direction. Under what condition will the amplitude of the resultant wave be greater than either of the two original waves? (a) in all cases (b) only if the waves have no difference in phase (c) only if the phase difference is less than 90 (d) only if the phase difference is less than 120 (e) only if the phase difference is less than 180arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author: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 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
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, Technology ...
Physics
ISBN:9781305116399
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
What Are Sound Wave Properties? | Physics in Motion; Author: GPB Education;https://www.youtube.com/watch?v=GW6_U553sK8;License: Standard YouTube License, CC-BY