Question

By wiggling one end, a sinusoidal wave is made to travel along a stretched string that has a mass per unit length of 22.0 g/m. The wave may be described by the wave function y 0.20 sin (0.90x-42) where x and y are in meters and t s in seconds. 1. (a) Determine the speed of the wave. Is the wave moving in the +x direction or the -x direction? b) What is the tension in the stretched string? (c) Determine the wavelength of the wave. (d) Determine the frequency with which the one end is wiggled. (e) Determine the period of the oscillations in the wave. (f) Determine the maximum transverse speed of a point in the string. (g) Determine the power transmitted by the wave. A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m << M. (a) If the period of oscillations for the pendulum is T, derive an expression for the speed of a transverse wave in the string when the pendulum hangs at rest in terms of m, M, Tand g (the acceleration due to gravity). Your expression should not include L. (b) If the string is made to vibrate at a frequency f, what is an expression for the wavelength of the wave in the string in terms of f, m, M, T and g? 2.

Answer 1

Concept: here we use the properties of wave motion on a string,

Concept: here we use the properties of wave motion on a string, K = 0.9 m^-1 w = 42s^-1 so, V = w/k = 46.67 m/s It is moving in +x - direction T = mu v^2 = (22 times 10^-3 kg/m) v^2 = 47.91 N lambda = 2 pi/k = 2 lambda/0.9 m^-1 = 6.98 m f = w/2 pi = 6.68 Hz Period = 1/f = 0.1496 s V_max = Aw, A = 0.2m, w = 425^-1 = 8.4 m/s P = 1/2 w^2 A^2 T/V = 1/2 (42s^-1)^2 (0.2 m)^2 (47.91 N)/(46.67 m/s) = 36.22 W

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