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* Open vs Closed pipes (Flutes vs Clarinets) This page compares the acoustics of open and closed cylindrical pipes, as exemplified by flutes and clarinets, respectively. An introduction to the woodwind family (and to sound waves) is given in This site discusses only cylindrical pipes. Instruments such as saxophones and oboes have approximately conical bores.

For the behaviour of cones compared with cylinders (and the wave patterns in flutes, clarinets, oboes etc), see. For a background about standing waves, see from. The flute (photo at left) is a nearly cylindrical instrument which is open to the outside air at both ends. The player leaves the embouchure hole open to the air, and blows across it. The clarinet (right) is a roughly cylindrical instrument which is open to the outside air at the bell, but closed by the mouthpiece, reed and the player's mouth at the other end.

The two instruments have roughly the same length. The bore of the clarinet is a little narrower than that of the flute, but this difference is not important to the argument here. We compare open and closed pipes in three different but equivalent ways then examine some complications. • • • • • • Standing wave diagrams First let's make some approximations: we'll pretend a flute and clarinet are the same length. For the moment we'll also neglect, to which we shall return later.

The next diagram (from ) shows some possible standing waves for an open pipe (left) and a closed pipe (right) of the same length. The red line is the amplitude of the variation in pressure, which is zero at the open end, where the pressure is (nearly) atmospheric, and a maximum at a closed end. The blue line is the amplitude of the variation in the flow of air.

This is a maximum at an open end, because air can flow freely in and out, and zero at a closed end. These are what we call the boundary conditions. Open pipe (flute). Nvram database file mt6752 vs mt6753.

Note that, in the top left diagram, the red curve has only half a cycle of a sine wave. So the longest sine wave that fits into the open pipe is twice as long as the pipe. A flute is about 0.6 m long, so it can produce a wavelength that is about twice as long, which is about 2L = 1.2 m. The longest wave is its lowest note, so let's calculate. Sound travels at about c = 340 m/s. This gives a frequency (speed divided by wavelength) of c/2L = 280 Hz.

Given the crude approximations we are making, this is close to the frequency of middle C, the lowest note on a flute. (See to convert between pitches and frequencies, and for more about flute acoustics.) Note that we can also fit in waves that equal the length of the flute (half the fundamental wavelength so twice the frequency of the fundamental), 2/3 the length of the flute (one third the fundamental wavelength so three times the frequency of the fundamental), 1/2 the length of the flute (one quarter the wavelength so four times the frequency of the fundamental). This set of frequencies is the (complete) harmonic series, discussed in more detail below. Closed pipe (clarinet).

The blue curve in the top right diagram has only quarter of a cycle of a sine wave, so the longest sine wave that fits into the closed pipe is four times as long as the pipe. Therefore a clarinet can produce a wavelength that is about four times as long as a clarinet, which is about 4L = 2.4 m. This gives a frequency of c/4L = 140 Hz – one octave lower than the flute. Now the lowest note on a clarinet is either the D or the C# below middle C, so again, given the roughness of the measurements and approximations, this works out. We can also fit in a wave if the length of the pipe is three quarters of the wavelength, i.e. If wavelength is one third that of the fundamental and the frequency is three times that of the fundamental.