Propagation constant k:
vp = λ/T = (2π/k)/(2π/ω) = ω/k
Two Velocities in a Traveling Wave
Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e.g., air or a string) and the velocity of the medium (the air or the string itself).
Consider a transverse wave traveling in a string. The mathematical form of the wave is
y(x,t) = Asin(Kx - wt)
Find the y velocity vy(x,t) of a point on the string as a function of x and t.
Express the y velocity in terms of w, A,k,x,and t.
Which of the following statements about, the x component of the velocity of the string, is true?
a) vx(x;t) = vp
b) vx(x;t) = vy(x;t)
c) vx(x;t) has the same mathematical form as vy(x;t) but is 180° out of phase.
d) vx(x;t) = 0
Find the slope of the string as a function of position x and time t.
Express your answer in terms of A,k,w, x,and t.