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PHY 711 Problem Set #14: Wave Equation with Initial Value Information for a Uniform Wire, Assignments of Physics

A problem set from a university physics course, phy 711, focusing on the wave equation for a uniform wire with given initial value information. Students are required to use maple or other software to find the analytic form of the function and plot the function and its derivative at two different time instances.

Typology: Assignments

Pre 2010

Uploaded on 08/16/2009

koofers-user-las
koofers-user-las 🇺🇸

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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=c22f
∂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.

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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 ∂^2 f ∂t^2

= c^2

∂^2 f ∂x^2

In this equation, c represents 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=

sinh(x) cosh^2 (x)

(a) Use Maple or other software to plot f (x, t)ct=0 and

∂f (x, t) ∂t

t=

(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.