The equation of a travelling wave is y = 60 cos (180 t

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The equation of a travelling wave is
y = 60 cos (180 t – 6x)
where y is in microns, t in second and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

y = 60 cos (180t – 6x) ....(1)

ω = 180, k = 6 ⇒	2π	= 6
	λ

v =	ω	=	2π	×	ω	=	180	= 30 m/s
	k		T		2π		6

Differentiating (1) w.r.t. t,

v =	dy	= -60 × 180 sin(180t - 6x)
	dt

v_max = 60 × 180 μm/s
= 10800 μm/s = 0.0108 m/s

	v_max	=	0.0108	= 3.6 × 10^-4
	v		30