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 λ.

A) Calculate the maximum transverse velocity of the point located at x=λ/2.
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. vmax =
B) Calculate the maximum transverse acceleration of the point located at x=λ/2.
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. amax =
C) What is the amplitude of the motion at the point located at x=λ/2?
Express your answer in terms of the variables v, f, A, λ, and appropriate constants.
ASW = D) 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=λ/2?
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. t =

Answer 1

A) The maximum transverse velocity of the point located at x=λ/2 is given by vmax = 2πfA.

B) The maximum transverse acceleration of the point located at x=λ/2 is given by amax = (2πf)^2A.

C) The amplitude of the motion at the point located at x=λ/2 is half the amplitude of the entire wave, so the amplitude at this point is A/2.

D) The time it takes for the string to go from its largest upward displacement to its largest downward displacement at the point located at x=λ/2 is given by t = 1/f.