Slit Drum Acoustics

What is modelled

A slit drum is a hollowed log with a long slit. Struck on a lip, it makes sound in two ways: the air inside the log and slit behaves like a bottle, a Helmholtz resonator, while each lip is a wooden bar clamped at one side and free at the other that rings at its own pitch. Lips of different thickness give two different notes, the signature of the lenga.

Equations

• Helmholtz f = (c / 2π) √(A / (V Leff)) with slit area A, cavity volume V and neck length Leff = t + 1.7 req.
• Cantilever bar f = (βL)² / (2π L²) √(E h² / (12 ρ)) with cos(βL) cosh(βL) = −1, so βL = 1.8751.
• Struck sound p(t) = Σ ak e−π fk t / Qk sin(2π fk t).

Checks run in the page

• The resonator integrated as a damped mass and spring with RK4 against the analytic frequency.
• The cantilever root found by bisection.
• A windowed Fourier transform of the synthesised sound against the model tones.
• The scaling laws of the cavity length and lip thickness.

Honest simplifications

The slit is treated as a short neck with a simple end correction, the cavity as a cylinder, the lips as uniform strips of dry hardwood, and the quality factors are fixed typical values. Coupling between the cavity and the lips, wood anisotropy and radiation are ignored, so the tones are indicative, not a tuning recipe for a real drum.

• Press Narrow slit, low hum to hear the cavity tone fall as the slit closes.
• Press Matched lips to make the two lips ring at one pitch.
• Thin one lip with the slider and watch the interval in cents change.