All Problems Elastic Waves. Acoustics.
Problem 4.170
Find the number of possible natural oscillations of air column in a pipe whose frequencies lie below \(v_{0}=1250 \mathrm{~Hz} .\) The length of the pipe is \(l=85 \mathrm{~cm} .\) The velocity of sound is \(v=340 \mathrm{~m} / \mathrm{s}\). Consider the two cases: (a) the pipe is closed from one end; (b) the pipe is opened from both ends. The open ends of the pipe are assumed to be the antinodes of displacement.
4.170. (a) \(v_{n}=\frac{v}{4 l}(2 n+1),\) six oscillations; (b) \(v_{n}=\frac{v}{2 l}(n+1)\) also six oscillations. Here \(n=0,1,2, \ldots\)