CALC Speed of Propagation vs. Particle Speed. ?(a) Show that Eq. (15.3) may be written as (b) Use y(x, t) to find an expression for the transverse velocity of a particle in the string on which the wave travels. (c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed u?Less than u? Greater than u?

Solution 12E Equation 15.3 is given as, y(x,t) = Acos[2f( t)] v (a) Let us simplify this equation. y(x,t) = A cos[2f( xv)] v 2f y(x,t) = A cos[ v (x vt)] y(x,t) = A cos[ vT(x vt)] (since frequency f = 1/Time period) y(x,t) = A cos[ (x vt)] (since wavelength = vT ) …..(1) This is the required form we need to find. Now, the equation (1) can also be written as, 2 y(x,t) = A cos(kx t) …..(2), where k = and 2v/ = 2f = (b)...