| Variations on standard exam questions are also possible, to give a better indication of whether students actually understand the derivation. The following question explores the transport of energy by a pulse: |
|
A wave of arbitrary shape moves to the right with a speed
v along a string with mass per unit length 
and tension T as shown. (Assume small displacements.) Figure 5 shows a snapshot
of the string at time t1.
(a) When a pulse travels to the right along a string, energy is transported to the right. In terms of work, force, and displacement, explain how energy passes the point x0
(b) At time t1, in what direction is the segment of string 
x moving?
(c) At this instant, what force is being exerted on it by the string to its left?
(d) By considering the direction of the force due to tension at different points on a pulse, show that the direction of the transverse component is always given correctly by the relationship
(e) As a sinusoidal wave travels along a string, is the rate at which energy passes a point constant with time?
(f) If not, for which displacements of the string is it greatest?
