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),
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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.
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