A sinusoidal transverse wave of wavelength 22.0 cm travels along a string in the

Question

A sinusoidal transverse wave of wavelength 22.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given as a function of time t. The scale of the vertical axis is set by ys = 6 cm. The wave equation is to be in the form of

y = ym sin(kx - wt + phi).

What are (a) the wave speed (speed of the wave along the string) and (b) the transverse velocity of the particle at x = 0 when t = 3.00 s?

*The graph is located in question 11 of Chapter 16. 

Explanation / Answer

= 22.0 cm, k = 2/, from the graph, period T = 14 s, = 2/T

y = 6 sin(2x/ - 2t/T + )

note at x = 0, t = 0, dy/dt > 0 (from the graph)

dy/dt = -6*2/T cos > 0, =

so y = 6 sin(2x/ - 2t/T + ) = 6 sin(x/11 - t/7 + )

a) wave speed v = /T = 1.57 cm/s

b) dy/dt = -6/7 cos(x/11 - t/7 + )

at x = 0, t = 3.00 s

dy/dt = -6/7 cos(-*3.00/7 + ) = 0.599 cm/s

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