October 10, 2007
PHY 711 – Problem Set # 14
Start reading Chapter 7 in Fetter and Walecka.
1. Suppose that you have a very long uniform wire stretched along the x-axis with constant
tension. To a very good approximation, transverse waves are described by vertical
displacements (with respect to equilibrium) by a function f(x, t) which satisfies a wave
equation
∂2f
∂t2=c2∂2f
∂x2.(1)
In this equation, crepresents a known constant which depends on the tension and
the mass per unit length of the wire. Also suppose that the following initial value
information is known:
f(x, t)ct=0 = 0.(2)
∂f (x, t)
∂t %t=0
=−sinh(x)
cosh2(x).(3)
(a) Use Maple or other software to plot f(x, t)ct=0 and ∂f(x, t)
∂t %t=0
.
(b) Find the analytic form of f(x, t) for some t > 0.
(c) Use Maple or other software to plot f(x, t) and ∂f(x, t)
∂t for at least two values of
t > 0.