A transverse sinusoidal wave of wavelength 20 cm is moving along a string in the

Question

A transverse sinusoidal wave of wavelength 20 cm is moving along a string in the positive x direction. The transverse displacement of the string particle at x -0 as a function of time is shown in figure below. (a) Make a rough sketch of one wavelength of the wave (the portion between x = 0 and x = 20 1. cm) at time t = 0. (b) What is the speed of the wave? (c) Write the equation for the wave with all the constants evaluated (d) what is the transverse velocity of the particle at x = 0 at t = 5.0 s? 4.0 t (s) -4.0 10

Explanation / Answer

speed v = wavelength/time period

wavelength = 20 cm

time period T = 10 s

speed v=20/10 = 2 cm/s

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wave equation y = A*sin(kx - wt)

A = amplitude = 4 cm

k = 2pi/wavelength = 2pi/20 = pi/10 = 0.314 m-1

w = 2pi/T = 2pi/10 = 0.628 rad/s

y = (4.0cm)sin( 0.314x - 0.628 t)

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v = dy/dt

v = -4*cos(0.314x - 0.628t)*0.628

at t = 5 s for x = 0

v = -4*cos(0 - 0.628*5)*0.628

v = -2.51 cm/s <<<<<-----ANSWER

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