A horizontal string tied at both ends is vibrating in its fundamental mode. The

Question

A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed v, frequency f, amplitude A, and wavelength lambda. Calculate the maximum transverse velocity of the point located at x = lambda /8. Calculate the maximum transverse acceleration of the point located at x = lambda /8. What is the amplitude of the motion at the point located at x = lambda /8? How much time does it take the string to go from its largest upward displacement to its largest downward displacement at the point located at x = lambda /8?

Explanation / Answer

A)

A' = 2A sin(kx) = 2A sin((2/)*(/8)) = 2A sin(/4) = 2A (2/2) = (2) A

v_max = 2A = 2A (2 f) = (2 2) A f

b)

a_max = 2A ^2 = (4 2) A ^2 f^2

c)

amplitude = 2 A

d)

t = T/2 = (1/f)/2 = 1/(2f)

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