EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
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Chapter 30, Problem 45P
To determine
The proof that any function of form
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Consider two wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx + ωt + ϕ) . What is the wave function resulting from the interference of the two wave? (Hint: sin (α ± β)= sin α cos β ± cos α sin β and ϕ = ϕ/2 + ϕ/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:
What is the direction of propagation of the wave de scribed in the wave function *
rad
y = (0.30 m) sin (12)
|t + (10 m-1)x|
O (A) left to right
O (B) right to left
O (C) top to bottom
(D)diagonal
Chapter 30 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 30 - Prob. 1PCh. 30 - Prob. 2PCh. 30 - Prob. 3PCh. 30 - Prob. 4PCh. 30 - Prob. 5PCh. 30 - Prob. 6PCh. 30 - Prob. 7PCh. 30 - Prob. 8PCh. 30 - Prob. 9PCh. 30 - Prob. 10P
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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.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_forwarddocs.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_forward
- a° y(z,t) 1 d*y(x,t) Which of the following wave functions satisfies the wave equation? A.) y(x, t) = A cos(kæ + wt) B.) y(x, t) = A sin(kx +wt) C.) y(x, t) = A[cos(kæ) + cos(wt)] For any of the equations above that satisfy the wave equation what are the transverse velocity and acceleration of a particle at point x?arrow_forward(a) What is the speed of the wave (b) What is the displacement of a particle at λ/2. (c) What is the maximum displacement of the wave? y = 2.1sin( 397t +9.23x)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_forward
- Consider two waves defined by the wave functions y1(x,t)=0.50m sin(2π/3.00mx+2π/4.00s t) y1(x,t)= and y2(x,t)=0.50msin(2π/6.00mx−2π/4.00st). What are the similarities and differences between the two waves?arrow_forwardShow that p(t, x) = A sin (ωt − kx + φ) satisfies the wave equation.arrow_forwardIf y(x,t)=sin(5pi x-2t) is the equation of the amplitude of the 1-D traveling wave determine the amplitude and wavelength and frequency and period and direction.arrow_forward
- Prove by direct substitution that a Gaussian pulse given by y(x;t)=0.5e^[-(x-5t)^2] in MKS units is NOT the solution of wave equation (5 ∂x-∂t) y(x;t)=0.arrow_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_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
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