A cylindrical organ pipe long is open at both ends

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

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: (i) Calculate the fundamental frequency of the pipe at 20∘C20^{\circ}\text{C}. (ii) Determine the frequency of the second overtone at 20∘C20^{\circ}\text{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).

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