Another wave problem

WASD

2013-11-25 1:57 am

A wave propagates along a taut string at a speed of 2 m/s along positive x direction.

At x=0.5 m the string element’s displacement is described by y=0.2sin(pi*t+pi/12) .

Find out the acceleration of a string element at x=0 as a function of time.

回答 (1)

天同

2013-11-25 3:39 am

✔ 最佳答案

Compare the given equation at x = 0.5 m with the general wave equation, we have
angular frequency w = pi
k(0.5) + p = pi/12
where k is the wave no = 2.pi/入

Because w = 2.pi.f = pi
frequency f = pi/(2.pi) = 1/2 Hz
入= 2/(1/2) m = 4 m
hence k = 2.pi/4 m^-1 = pi/2 m^-1

Thus, (pi/2)(0.5) + p = pi/2
p = pi/4

The wave equation thus is: y = 0.2sin(pi.t + (pi/12)x + pi/2)
At x = 0, the equation becomes,
y = 0.2sin(pi.t + pi/2)
acceleration = d^2y/dt^2 = -(pi)^2(0.2).sin(pi.t+pi/2)

2013-11-24 20:41:48 補充：
p is the phas angle, and 入 is the wavelength.

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