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發問:
An open organ pipe has two adjacent natural frequencies of 500 and 600 Hz. Assume the speed of sound in air is 340m/s. What is the length of the organ pipe?
最佳解答:
Let n be the no. of loops in the open pipe when the frequency is 500 Hz, and L be the length of the pipe. Hence, L = (n/2)入 where 入 is the wavelength of sound in the pipe i.e. 入 = 2L/n Since speed of sound = frequency x wavelength 340 = 500 x (2L/n) ---------------- (1) At the next higher frequency of 600 Hz, no. of loops = n +1 hence, L= [(n+1)/2]入 or 入= 2L/(n+1) and 340 = 600 x 2L/(n+1) -------------- (2) Equating (1) and (2), 500 x (2L/n) = 600 x 2L/(n+1) 500/n = 600/(n+1) solve for n gives n = 5 Substitute n =5 into (1), 340 = 500 x (2L/5) thus L = 1.7 m
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