Seismic waves are used to infer properties of subsurface geological structures, where sound is propagated by small elastic vibrations. Assume a simple model where the elastic medium is stretched between points x 0 and x=5. At time t= 0, the elastic medium is at rest and the velocity of the elastic medium is kept uniform at 10. The 1-dimensional wave equation is given as follows: du = 2- for all 00 %3D (a) Describe the initial and boundary conditions of the wave equation in this scenario. (b) Hence, deduce the displacement function u(x,t) of the elastic medium, subject to the conditions in (a).
Seismic waves are used to infer properties of subsurface geological structures, where sound is propagated by small elastic vibrations. Assume a simple model where the elastic medium is stretched between points x 0 and x=5. At time t= 0, the elastic medium is at rest and the velocity of the elastic medium is kept uniform at 10. The 1-dimensional wave equation is given as follows: du = 2- for all 00 %3D (a) Describe the initial and boundary conditions of the wave equation in this scenario. (b) Hence, deduce the displacement function u(x,t) of the elastic medium, subject to the conditions in (a).
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Transcribed Image Text:Seismic waves are used to infer properties of subsurface geological structures, where
sound is propagated by small elastic vibrations. Assume a simple model where the elastic
medium is stretched between points x = 0 and x=5. At time t= 0, the elastic medium is
at rest and the velocity of the elastic medium is kept uniform at 10.
The 1-dimensional wave equation is given as follows:
a'u
= 2 for all 0<x<5 and t>0
(a)
Describe the initial and boundary conditions of the wave equation in this scenario.
(b)
Hence, deduce the displacement function u(x,t) of the elastic medium, subject to
the conditions in (a).
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