Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 17, Problem 64PQ
To determine
To prove the expression for the wave equation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
On a real string of linear density μ, some of the energy of the wave dissipates as the wave travels down the string. Such a
situation can be described by a wave function y (x, t) whose amplitude A(x) depends on the position x, by
y (x, t) = A(x) sin(kx – wot), where A(x) = (Age¯b¾, for constant values AQ and b.
Derive an expression for the average power P(x) transported
by the wave as a function of x, where x > 0.
P(x) =
The period of oscillation T of a water surface wave isassumed to be a function of density ρ , wavelength l , depth h , gravity g , and surface tension Y . Rewrite this relationshipin dimensionless form. What results if Y is negligible?Hint: Take l , ρ , and g as repeating variables.
Problem 5
(a) show that the following function satisfies the wave equation (this is a spherical wave). Show
that its velocity is velocity v = **
f(r,t) = C = cos(kr - wt)
The wave fronts are spherical shells at radius r that propagate outward from the origin; the
amplitude of the disturbance decreases as the distance from the source.
For this, use the Laplacian in spherical coordinates:
1 0
√²f=
Acoustic Monopole
af
1 მ
r²sine de
sinė
1 a²ƒ
r²sin²0 04²
Chapter 17 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 17.2 - As weve seen before, terms used in physics often...Ch. 17.2 - A graph of a pulses profile and a...Ch. 17.3 - Prob. 17.3CECh. 17.5 - Prob. 17.4CECh. 17.5 - The bulk modulus of water is 2.2 109 Pa (Table...Ch. 17.6 - Prob. 17.6CECh. 17 - A dog swims from one end of a pool to the opposite...Ch. 17 - Prob. 2PQCh. 17 - Prob. 3PQCh. 17 - Prob. 4PQ
Ch. 17 - Prob. 5PQCh. 17 - Prob. 6PQCh. 17 - Prob. 7PQCh. 17 - Prob. 8PQCh. 17 - A sinusoidal traveling wave is generated on a...Ch. 17 - Prob. 10PQCh. 17 - Prob. 11PQCh. 17 - The equation of a harmonic wave propagating along...Ch. 17 - Prob. 13PQCh. 17 - Prob. 14PQCh. 17 - Prob. 15PQCh. 17 - A harmonic transverse wave function is given by...Ch. 17 - Prob. 17PQCh. 17 - Prob. 18PQCh. 17 - Prob. 19PQCh. 17 - Prob. 20PQCh. 17 - Prob. 21PQCh. 17 - Prob. 22PQCh. 17 - A wave on a string with linear mass density 5.00 ...Ch. 17 - A traveling wave on a thin wire is given by the...Ch. 17 - Prob. 25PQCh. 17 - Prob. 26PQCh. 17 - Prob. 27PQCh. 17 - Prob. 28PQCh. 17 - Prob. 29PQCh. 17 - Prob. 30PQCh. 17 - Prob. 31PQCh. 17 - Problems 32 and 33 are paired. N Seismic waves...Ch. 17 - Prob. 33PQCh. 17 - Prob. 34PQCh. 17 - Prob. 35PQCh. 17 - Prob. 36PQCh. 17 - Prob. 37PQCh. 17 - Prob. 38PQCh. 17 - Prob. 39PQCh. 17 - Prob. 40PQCh. 17 - Prob. 41PQCh. 17 - Prob. 42PQCh. 17 - Prob. 43PQCh. 17 - Prob. 44PQCh. 17 - Prob. 45PQCh. 17 - What is the sound level of a sound wave with...Ch. 17 - Prob. 47PQCh. 17 - The speaker system at an open-air rock concert...Ch. 17 - Prob. 49PQCh. 17 - Prob. 50PQCh. 17 - Prob. 51PQCh. 17 - Prob. 52PQCh. 17 - Prob. 53PQCh. 17 - Using the concept of diffraction, discuss how the...Ch. 17 - Prob. 55PQCh. 17 - Prob. 56PQCh. 17 - An ambulance traveling eastbound at 140.0 km/h...Ch. 17 - Prob. 58PQCh. 17 - Prob. 59PQCh. 17 - Prob. 60PQCh. 17 - Prob. 61PQCh. 17 - In Problem 61, a. Sketch an image of the wave...Ch. 17 - Prob. 63PQCh. 17 - Prob. 64PQCh. 17 - Prob. 65PQCh. 17 - Prob. 66PQCh. 17 - Prob. 67PQCh. 17 - Prob. 68PQCh. 17 - Prob. 69PQCh. 17 - Prob. 70PQCh. 17 - A block of mass m = 5.00 kg is suspended from a...Ch. 17 - A The equation of a harmonic wave propagating...Ch. 17 - Prob. 73PQCh. 17 - Prob. 74PQCh. 17 - Prob. 75PQCh. 17 - Prob. 76PQCh. 17 - A siren emits a sound of frequency 1.44103 Hz when...Ch. 17 - Female Aedes aegypti mosquitoes emit a buzz at...Ch. 17 - A careless child accidentally drops a tuning fork...Ch. 17 - Prob. 80PQCh. 17 - A wire with a tapered cross-sectional area is...
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
- A uniform plane wave has the generic expression Φ(z,t) = A cos(ωt – kz + δ) with the following given parameter values: wave amplitude = 10, wave frequency in Hz f = 500 Hz, phase velocity vph = 10 m/s, and the phase angle δ = 60o. Find the values of the parameters A, ω, and k. ..arrow_forwardShow that a standing wave given by the equation: y (x, t) = A sin (kx) sin (ωt) satisfies the wave equation, verify that: v0 = ω / k; shows that the standing wave also satisfies the equation of harmonic oscillator: ∂2y(x,t)/∂t2 = −ω2y(x,t), interpret this result.arrow_forwardA wave has the form y=Acos((2pix/lambda)+(pi/3)) when x<0. For x>0, the wavelength is lambda/2. By applying continuity conditions at x=0, find the amplitude (in terms of A) and phase of the wave in the region x>0. Sketch the wave, showing both x<0 and x>0.arrow_forward
- A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 5. Find the resultant wave function analytically. 6. Study how the resulting wave…arrow_forwardConsider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then: A. Calculate the period τ and the optical frequency v for green light? B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2). C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.arrow_forwardA wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency.arrow_forward
- Another Wave Equation With Damping Determine the specific solution to the wave equation with damping ди(х, 1) Ə²u(x,t) ôx² ô²u(x,t) + 4 for 0 < x < n and 0 < t, given also the BCs: u(0,t) initial conditions O and u(n,t) = 0 for 0 < t and the ôu(x,t) u(х,0) : = x and -0arrow_forwardProblem 4: A traveling wave along the x-axis is given by the following wave functionψ(x, t) = 3.6 cos(1.4x - 9.2t + 0.34),where x in meter, t in seconds, and ψ in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this plane wave: Part (a) The amplitude in meters. Part (b) The frequency, in hertz. Part (c) The wavelength in meters. Part (d) The wave speed, in meters per second. Part (e) The phase constant in radians.arrow_forwardShow explicitly that the wave function, y (x, t) A cos(kx - wt), = satisfies the wave equation, 8² dx 2 y (x, t) = 1 8² v² Ət2 y(x, t). Write the explicit value of v as a function of the parameters of the wave function, w, k and A.arrow_forward
- A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t = t0 is given by g(x, t0) = A sin(x/a). Write the wave equation for a general time t.arrow_forwardWrite the real and complex expression for a plane wave E2 propagating at an angle of 60° with respect to the z axis on the xz plane. The wavelength of is 1550 nm, and the speed is c = c/1.45.arrow_forwardA block of mass m, attached to a spring of force constant k, undergoes a simple harmonic motion on a horizontal frictionless surface. The mechanical energy of the block-spring system is E = 2.3 J. If its maximum speed is v_max = 2 m/s, then its mass is: Om = 1.28 kg m = 1.15 kg m = 0.8 kg Om = 1.38 kg ted by the wave function: y(x,t) = A sin (kx - wt + p).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
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