Resonance can also occur in pipes which are open at both ends.

Consider a source of sound close to one end of a pipe, of length, , as shown below.

At an open end, waves are reflected without a change of phase. So, if waves travel twice the length of the pipe in one time period, they will return to the source in phase and constructive interference (resonance) will occur.

At each end we have a large amplitude vibration: an anti-node of the stationary wave.

The fundamental resonance is represented on the next diagram.

In this case,	= l/2
In general	l = v/f

therefore, the fundamental frequency, f_o, is given by

The next two resonances are shown below.

In general, for a pipe open at both ends

• Resonance in Closed Pipes

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