The displacement, L of particles in a wave travelling along the x-axis is given by, y(x,t) = 2xe¬x-3t + 6t e¬x-3t for x and y measured in çentimeters and t in seconds. (a) Use the one-dimensional wave equation to determine the phase speed of the wave. In what direction does the wave propagate? (b) Show that a particle at any position x along the wave obeys the equation of motion, a²y at² ду + 6. + 9y = 0 at What kind of oscillation does this describe?
The displacement, L of particles in a wave travelling along the x-axis is given by, y(x,t) = 2xe¬x-3t + 6t e¬x-3t for x and y measured in çentimeters and t in seconds. (a) Use the one-dimensional wave equation to determine the phase speed of the wave. In what direction does the wave propagate? (b) Show that a particle at any position x along the wave obeys the equation of motion, a²y at² ду + 6. + 9y = 0 at What kind of oscillation does this describe?
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Transcribed Image Text:The displacement, y of particles in a wave travelling along the x-axis is given by,
y(x,t)
= 2xe-x-3t + 6t e¬x-3t
for x and y measured in centimeters and t in seconds. (a) Use the one-dimensional wave equation to
determine the phase speed of the wave. In what direction does the wave propagate? (b) Show that a
particle at any position x along the wave obeys the equation of motion,
a²y
ду
+6+9y = 0
at
at²
What kind of oscillation does this describe?
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