Two velocities in a traveling wave
wave motion is characterized bytwo velocities: the velocity with which the wave moves in themedium (e. g., air or a string) and the velocity of the medium (theair or the string itself).
consider a transverse wavetraveling in a string. the mathematical form of the wave is
y(x, t) = a \sin(kx-\omega t)
part a. find the velocity of propagationv_p of this wave.
express the velocity ofpropagation in terms of some or all of the variables a, k, and omega.
part b. find the y velocity v_y(x, t) of a point on the string as a function ofxand t.
express the y velocity interms of omega, a, k,x, and t.
part c. which of the following statements aboutv_x(x, t), the x component of the velocity of thestring, is true?
v_x(x; t) = v_{\rm p}
v_x(x; t) = v_y(x; t)
v_x(x; t) has the same mathematical form as v_y(x; t) but is 180^\circ out of phase.
v_x(x; t)=0
part d. find the slope of the string \frac{\partial{y(x, t)}}{\partial{x}} as a function of position x and time t.
express your answer in terms ofa, k,omega, x, and t.