A transverse wave on a string is described by the following wave function. y = 0

Question

A transverse wave on a string is described by the following wave function. y = 0.105 sin (pi/12x + 3 pi t) where x and y are in meters and t is in seconds. (a) Determine the transverse speed at t = 0.260 s for an element of the string located at x = 1.50 m. m/s (b) Determine the transverse acceleration at t = 0.260 s for an element of the string located at x = 1.50 m. m/s^2 (c) What is the wavelength of this wave? m (d) What is the period of this wave? s (e) What is the speed of propagation of this wave? m/s

Explanation / Answer

A.

v = dy/dt

v = 3*pi*0.105*cos (pi*x/12 + 3*pi*t)

when t = 0.26 and x = 1.5 m

v = 3*pi*0.105*cos (pi*1.5/12 + 3*pi*0.26) = -0.945 m/sec

B.

a = dv/dt

a = -9*pi^2*0.105*sin (pi*x/12 + 3*pi*t)

when t = 0.26 and x = 1.5 m

v = -9*pi^2*0.105*sin (pi*1.5/12 + 3*pi*0.26) = -2.742 m/sec

C.

k = 2*pi/lambda

pi/12 = 2*pi/lambda

lambda = 24 m

D.

w = 2*pi/T

3*pi = 2*pi/T

T = 1.5 sec

E.

Speed of propagation = lambda/T = 24/1.5 = 16 m/sec

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