   Chapter 16, Problem 20P Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Solutions

Chapter
Section Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

Show that the wave function y = ln [b(x − vt)] is a solution to Equation 16.27, where b is a constant.

To determine

That the wave function y=ln[b(xvt)] is a solution to the linear wave equation in general.

Explanation

Any function is a solution of linear wave equation in general if it satisfies the equation completely.

The linear wave equation in general is,

2yx2=1v22yt2

The given wave function is,

y=ln[b(xvt)]        (I)

Differentiate equation (I) partially with respect to x.

yx=x(ln[b(xvt)])=1b(xvt)×b=1(xvt)

Again differentiate partially with respect to x.

2yx2=x{1(xvt)}=1(xvt)2        (II)

Differentiate equation (I) partially with respect to t

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