Question 10 A sinusoidal transverse wave is traveling along a string in the nega

Question

Question 10 A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 2.0 N, and its linear density is 33 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave. (e) Find the maximum transverse speed of a particle in the string. If the wave is of the form y(x,t) = Ym sin(kx wt + psi), what are (f) k, (g) w, and (h) psi, and (j) the correct choice of sign in front of co? (a) Number Units (b) Number Units (C) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units

Explanation / Answer

a) The maximum vertical distance is amplitude A = 4cm or 0.04m

b) Wavelength is the horizontal distance of wave (crest & trough) = 40cm or 0.4m

c) Speed of wave V = sqrt [ T/ u ] = sqrt [2 / 33x10^-3 ] = 7.785 m/s

d) T = Wavelength / speed = 0.4m / 7.785 = 0.0514s or 51.4 milliseconds

e) Maximum speed of particle Vm = 2 pi (A) / T = 2(3.14)(0.04m) / 0.0514s = 4.891m/s

f) k = 2 pi / wavelength = 2 (3.14) / 0.4m = 15.7

g) w = 2 pi / T = 2 (3.14) / 0.0514 = 122.3 rad/s

h) as the wave is moving to the left the direction is considered as positve.

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