A string oscillates according to the equation. What are the (a) amplitude and (b

Question

A string oscillates according to the equation. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 2.18 cm when t = 1.19 s?

A string oscillates according to the equation. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 2.18 cm when t = 1.19 s? Y' = (0.402 cm) sin[( pi / 5.0 cm-1 )x] cos[(22.7 pi s-1)t].

Explanation / Answer

a)

A =0.402 cm/2 =0.201 cm

b)

V=W/K =22.7pi/(pi/5)

V=113.5 cm/s

c)

lambda =2pi/K =2pi/(pi/5)

lambda =10 cm

d=lambda/2 =10/2

d=5 cm

d)

u=dy/dt =-(0.402)sin[(pi/5)x] (22.7pi)sin[(22.7pi)t]

u=-28.67 sin[(pi/5)*2.18]sin(22.7pi*1.19)

u=1.147 cm/s

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