The string shown in the figure is driven at a frequency of 5.00 Hz. The amplitud

Question

The string shown in the figure is driven at a frequency of 5.00 Hz. The amplitude of the motion is A = 10.5 cm, and the wave speed is v = 19.5 m/s. Furthermore, the wave is such that y = 0 at x = 0 and t = 0. (a) Determine the angular frequency for this wave. _______ rad/s (b) Determine the wave number for this wave. __________ rad/m (c) Write an expression for the wave function. (Use the following as necessary: t, x. Let x be in meters and t be in seconds.) y = _____sin(_____) (d) Calculate the maximum transverse speed. _________ m/s (e) Calculate the maximum transverse acceleration of an element of the string. _________ m/s2

Explanation / Answer

a)f =5HZ

=2f =2*5=31.4rad/s

b)K=/v =31.4/19.5 =1.6 rad/m

C)Y(x,t) =Asin(kx-t) =0.105sin(1.6x-31.4t)

d)(y/t)max =A =0.105*31.4 =3.298m/s3.3m/s

e)(2y/t2) =A2 =0.105*31.42 =103.6m/s2

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