Question

The equation of a travelling wave is y(x, t) = 0.02 sin ((x)/(0.05) + (t)/(0.01)) m Find (a) the wave velocity and (b) the particle velocity at x = 0.2 m and t = 0.3 s. Given cos theta = -0.85, where theta = 34 rad

Answer 1

answer : option (a) 5m/s (b) -1.7 m/s

given, the equation of a traveling wave is y(x, t) = 0.02sin(x/0.05 + t/0.01 ) m

(a) find the wave velocity

we know, standard equation of wave, y = Asin(kx + ωt)

on comparing we get,

k = 1/0.05 and ω = 1/0.01

now wave velocity = ω/k

= (1/0.01)/(1/0.05) = 5 m/s

(b) find particle velocity at x = 0.2 m, and t = 0.3 sec

v = dy/dt = 0.02 × 1/0.01 cos(x/0.05 + t/0.01)

= 2cos(0.2/0.05 + 0.3/0.01)

= 2cos(4 + 30)

= 2cos(34)

= 2(-0.85)

= -1.7 rad/s

Answer 2

Answer:

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Explanation:

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