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

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter13: Continuous Systems; Waves
Section: Chapter Questions
Problem 13.22P
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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
Transcribed Image Text: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
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