Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 17, Problem 10PQ
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Consider two wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx + ωt + ϕ). The resultant wave form when you add the two functions is yR = 2A sin (kx +ϕ/2) cos (ωt + ϕ/2). Consider the case where A = 0.03 m−1, k = 1.26 m−1, ω = π s−1 , and ϕ = π/10 . (a) Where are the first three nodes of the standing wave function starting at zero and moving in the positive x direction? (b) Using a spreadsheet, plot the two wave functions and the resulting function at time t = 1.00 s to verify your answer.
Two sinusoidal waves of wavelength A= 2/3 m and amplitude A = 6 cm and
differing with their phase constant, are travelling to the right with same velocity v
= 50 m/s. The resultant wave function y res (xt) will have the form:
O y_res (x t) - 12(cm) cos(p/2) sin(3x-150nt=p/2).
O y res (xt) -12(cm) cos(o/2) sin(3x150T-0/2),
O y res (xt) 12(cm) cos(p/2) sin(150rtx-3Tt-0/2).
O y res (x,t) 12(cm) cos(o/2) sin(3x-180nt-0/2)
O y res (x,t) =12(cm) cos(o/2) sin(150nx-3rt-0/2),
Two sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 60 m/s. The resultant wave function y_res (x,t) will have the form:
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...
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- 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_forwardTwo sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: O y-res (x,t) = 12(cm) cos(p/2) sin(150tx-3rtt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3Tx-150t+4/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3Ttx-180rtt+p/2). O y-res (x,t) = 12(cm) cos(p/2) sin(150rtx+3rt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3Ttx+150rtt+p/2).arrow_forwardTwo sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v 50 m/s. The resultant wave function y res (x,t) will have the form:arrow_forward
- Show 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_forwardGiven the wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx − ωt + ϕ) with ϕ ≠ π/2 , show that y1 (x, t) + y2 (x, t) is a solution to the linear wave equation with a wave velocity of v = √(ω/k).arrow_forwardA standing wave is the result of superposition of two harmonic waves given by the equations y1(x;t) =Asin(ωt - kx) and y2(x; t) = Asin(ωt + kx). The angular frequency is ω = 3π rad/s and the k = 2πrad/m is the wave number.(a) Give an expression for the amplitude of standing wave.arrow_forward
- y2 = 0.01 sin(5rx+40rt), O y1 = 0.04 sin(20x-320nt); y2 = 0.04 sin(20TDX-+320rt), Two sinusoidal waves of wavelengthA = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: O y res (x,t) = 12(cm) cos(p/2) sin(3ttx+150rtt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3nx-180nt+p/2). y_res (x,t) = 12(cm) cos(p/2) sin(3nx-150nt+p/2). O y res (x,t) = 12(cm) cos(p/2) sin(150rtx-3nt+p/2). y_res (x,t) = 12(cm) cos(@/2) sin(150tx+3nt+p/2). Two identical sinusoidal waves with wavelengths of 1.5 m travel in the same. direction at a speed of 10 m/s. If the two waves originate from the same startingarrow_forwardA standing wave is the result of superposition of two harmonic waves given by the equations y1(x;t) =Asin(ωt - kx) and y2(x; t) = Asin(ωt + kx). The angular frequency is ω = 3π rad/s and the k = 2πrad/m is the wave number.(a) Give an expression for the amplitude of standing wave. b) calculate the frequency of the wavearrow_forwardA traveling wave on a long strong is described by the time-dependent wave function f(x, t) = a sin(bx - qt), with a = 6.00 x 10-2 m, b = 5? m-1, and q = 314 s-1. You want a traveling wave of this frequency and wavelength but with amplitude 0.0400 m. Write the time-dependent wave function for a second traveling wave that could be added to the same string in order to achieve this.arrow_forward
- docs.google.com/forms/d/e/1Ff o Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: y_res (x,t) = 12(cm) cos(4/2) sin(3Tx+150rt+p/2). y_res (x,t) = 12(cm) cos(4/2) sin(150Ttx+3nt+p/2). y_res (x,t) = 12(cm) cos(4/2) sin(150ttx- 3nt+p/2). y_res (x,t) = 12(cm) cos(4/2) sin(3tx- 150rtt+p/2). y_res (x,t) = 12(cm) cos(p/2) sin(3tx- 180nt+p/2). العربية الإنجليزية ... +arrow_forwardTwo sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the left with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: y_res (x,t) = 12(cm) cos(φ/2) sin(150πx+3πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx+150πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx-150πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx-180πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(150πx-3πt+φ/2).arrow_forwardA traveling wave is described by y = 10 sin (βz – ωt). Sketch the wave at t = 0 and at t = t1, when ithas advanced λ /8, if the velocity is 3 X 108 m/s and the angular frequency ω = 1 X 106 rad/s. Repeat for ω = 2 X 106 rad/s and the same t1.arrow_forward
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