Physics

Physics

Problem

A cylindrical organ pipe 1.20 m1.20\,\text{m} long is open at both ends. The speed of sound in air varies with temperature TT (in ∘C^{\circ}\text{C}) according to v=331+0.6T m s−1v = 331 + 0.6T\,\text{m}\,\text{s}^{-1}. Answer the following: a. (i) Calculate the fundamental frequency of the pipe at 20∘C20^{\circ}\text{C}. b. (ii) Determine the frequency of the second overtone at 20∘C20^{\circ}\text{C}. c. (iii) The air in the pipe is now heated uniformly to 35∘C35^{\circ}\text{C}. Find the percentage increase in the frequency obtained in part (ii).
Intuitive explanation

The fundamental frequency of an open pipe depends on both its length and the speed of sound traveling through it. Since sound speed changes with temperature, the pipe's resonant frequency will shift even though its physical length stays fixed. You'll use the relationship f=v2Lf = \frac{v}{2L} for the fundamental mode, then track how ff changes as temperature varies.

Intuitive explanation

The fundamental frequency of an open pipe depends on both its length and the speed of sound traveling through it. Since sound speed changes with temperature, the pipe's resonant frequency will shift even though its physical length stays fixed. You'll use the relationship f=v2Lf = \frac{v}{2L} for the fundamental mode, then track how ff changes as temperature varies.

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