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 = 0.095 sin ((x)(pi/12)  + (3)(pi)(t))

where x & y are in meteres and t is in seconds.

(a) Determine the transverse speed at t = 0.260 s for an element of the string located at x = 1.30 m.

(b) Determine the transverse acceleration at t = 0.260 s for an element of the string located at x = 1.30 m.

(c) What is the wavelength of this wave?

(d) What is the period of this wave?

(e) What is the speed of propagation of this wave?

Explanation / Answer

a) dy/dt = 0.095*3*pi*cos( x pi/12 + 3*pi*t) = 0.095*3*pi*cos(1.3*pi/12 + 3*pi*0.26)=-0.84 m/s

b) a = dv/dt = -0.095*(3*pi)^2*sin(x*pi/12 + 3*pi*t) =-0.095*(3*pi)^2*sin(1.3*pi/12 + 3*pi*0.26)=-2.9 m/s^2

c) k = pi/12 = 2 pi/lambda

lambda = 2 pi/(pi/12) = 24 m

d) 2 pi/T = 3 pi

2/T = 3

T = 2/3 s

e) v = lambda/T = 24/(2/3) = 36 m/s

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