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.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Waves on a String concept. You can view video lessons to learn Waves on a String. Or if you need more Waves on a String practice, you can also practice Waves on a String practice problems.