A travelling wave in a stretched string is described by the equation y = a sin (kx t). The maximum particle velocity is
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The maximum velocity of the particle is V = Aω
Explanation:
y = Asin ( Kx - ωt)
v = dy / dt = - A ωcos ( Kx - ωt) ----- (1)
Now
Maximum velocity "dv / dt = 0
dv / dt = - Aω^2 sin ( Kx - ωt) = 0
Sin ( Kx - ωt) = 0
( Kx - ωt) = 0
( Kx - ωt) = nπ
cos ( Kx - ωt) = ±1
V = Aω
Thus the maximum velocity of the particle is V = Aω
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