The designs of Helmholtz resonator (or only resonator) is characterized by the large cavity at its belly and a thin neck. See the picture below:

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It basically works on the theory of harmony. As the air (or any gas) tries to ram into the resonator through its neck, the pressure inside the cavity increases and the air bounces out, but while bouncing out quickly due to inertia, it creates a partial vacuum near the neck of the resonator and the air is again sucked in. The process continues like the phenomena of a ping-pong ball hitting the ground. The resonator acts like a shock absorber for the pressure waves.
The frequency of a resonator can be calculated as below:

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Frequency f = (c/2Π).√ (A/L.V)
Where,
c = the speed of sound.
L = length of the neck
A = area of the neck
V = cavity volume of the resonator