Appendix III

# Answers to problems

Problem 2.1.

From Eq. (2.112), we see that the eigenfrequencies of the pan flute are in multiples of 2n
+
1. In other words, they are in odd multiples, and the even ones are missing. The fundamental resonance frequency is given by f
=
c/(4l)
=
345/(4
×
0.294)
=
293
Hz.

From Eq. (2.94), we see that the eigenfrequencies of the pan flute are in multiples of n. In other words, they are in odd and even multiples. The fundamental resonance frequency is given by f
=
c/(2l)
=
345/(2
×
0.294)
=
587
Hz.

Problem 2.2.

In the steady state, the homogenous wave equation in cylindrical coordinates from Eq. (2.23) becomes

$(\frac{{\partial}^{2}}{\partial {w}^{2}}+\frac{1}{w}\xb7\frac{\partial}{\partial w}+$

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