Question

A pipe in air at 20.3°C is to be designed to produce two successive harmonics at 280 Hz and 320 Hz. How long must the pipe be?

Answer 1

If two successive harmonics differ by 40Hz, that means the fundamental frequency is 40Hz. The fundamental frequency is the lowest frequency that can be made by the pipe. Every harmonic you go up, you just add the fundamental frequency. So here we are looking at the 7th and 8th harmonics (40x7=280, 40x8=320).

The pipe is open, because this is the only way you can use all harmonics (and we need two consecutive ones). Closed pipes can only use odd or even harmonics (depending on if one or both ends is closed).

The speed of sound at 20.3 c is 343 m/s. Divide this by the fundamental frequency to get the corresponding wavelength. 343/40= 8.6 m. Now, for an open pipe, the pipe will be only one half of the wavelength of the fundamental frequency. So, the pipe is 4.3m.