Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 30, Problem 45P
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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 .)
Show that the wave equation y(x,t)=A cos(wt + kx) satisfies the wave equation.
(a) Show that the function y(x, t) = x2 + υ2t2 is a solution to the wave equation. (b) Show that the function in part (a) can be written as f(x + υt) + g(x - υt) and determine the functional forms for f and g. (c) What If? Repeat parts (a) and (b) for the function y(x, t) = sin (x) cos (υt).
Chapter 30 Solutions
Physics for Scientists and Engineers
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- 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_forwardshow that a function f=f(u), where w=x-vt, satisfies the wave equation: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
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