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A wave traveling along the x axis is described mathematically by the equation y = 0.19...

A wave traveling along the x axis is described mathematically by the equation y = 0.19 sin (8.1πt - 0.59πx), where y is the displacement (in meters), t is in seconds, and x is in meters. What is the speed of the wave?

answer in m/s

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Answer #1

  The standard form of the wave equation is

y = a sin 2π ( vt/λ - x/λ)

compare it with

y = 0.19 sin (8.5 π t - 0.59 π x)

or
y = 0.19 sin 2π( 8.5t/2 - o.59 x/2)

Hence,
v/λ = 8.5/2

1/λ = 0.59 /2

v = (8.5/2)*(2/0.59)

v = 14.40 m/s is the velocity of the traveling wave

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