A Helmholtz resonator is an air-filled chamber with an opening that resonates at a specific frequency:
f = \frac{c}{2\pi} \sqrt{\frac{A}{V L}}where:
f = target frequency (19 Hz)
c = speed of sound (~343 m/s at room temperature)
A = cross-sectional area of the port (m²)
V = volume of the resonator chamber (m³)
L = effective length of the port (m), including end correction
Calculate Required Volume (V)
For a 12" diameter sonotube (~30.48 cm), the internal volume per foot is:
V_{\text{tube, per foot}} = \pi \left(\frac{D}{2}\right)^2 H= 3.1416 \times \left(\frac{30.48}{2}\right)^2 \times 30.48 \approx 22.2 \text{ liters per foot}Thus, a 4-foot (48") sonotube has:
V_{\text{tube}} = 4 \times 22.2 = 88.8 \text{ liters} = 3.14 \text{ ft}^3This is a good resonating chamber size for a 19Hz tuning frequency.
Calculate the Port Dimensions
Using the Helmholtz resonance formula:
19 = \frac{343}{2\pi} \sqrt{\frac{A}{V L}}We assume an 8-inch diameter port (~20.32 cm):
A = \pi \left(\frac{20.32}{2}\right)^2 = 324.3 \text{ cm}^2 = 0.0324 \text{ m}^2
Solving for port length L:
L = \frac{A}{V} \left( \frac{343}{2\pi \times 19} \right)^2L = \frac{0.0888}{0.0324} \times \left(\frac{119.38}{343}\right)^2L \approx 9.8 \text{ inches} \approx 25 \text{ cm}Step 4: Final Design Summary
Sealed Box for Woofer: 1 ft³ plywood enclosure.
Sonotube Resonator: 12" diameter, 48" long, sealed at one end.
Port: 8-inch diameter, ~9.8 inches long, placed at the opposite end of the sonotube. Use sleeve to adjust.
Tuning Frequency: 19Hz, achieved via Helmholtz resonance.
