Helmholtz resonance and the shell
PHY-09What is Helmholtz resonance in plain terms?#
beginner
Short answer. It is the note you get when you blow across the top of a bottle. A container of air with a hole in it has a natural frequency, because the plug of air in the hole acts as a mass and the air inside the container acts as a spring. On a handpan the cavity is the bottle and the gu is the hole.The mechanism is a mass on a spring, and nothing more complicated than that. Push the plug of air in the neck inward and it compresses the air inside, which pushes back. The plug overshoots outward, the inside air is now rarefied and pulls it back, and the oscillation continues at whatever rate that particular mass and that particular springiness produce. The steel is not vibrating in this mode at all. It is the air doing the work.
The frequency is given by
f = (c / 2π) × √( A / (V × L) )
where c is the speed of sound in air, roughly 340 m/s, A is the cross sectional area of the port, V is the volume of the cavity and L is the effective length of the port neck. The effective length is a little longer than the physical neck, because air just outside and just inside the opening moves along with the plug; the usual correction is about 0.6 times the radius at the outer end and about one radius at the inner end.
Read off what the formula tells you. A bigger cavity gives a lower frequency, which is why a deep shell has a deeper gu tone than a shallow one of the same diameter. A bigger port gives a higher frequency, because more air mass moves per unit of pressure change. A longer or narrower neck gives a lower frequency, which is why makers curve the neck of the gu inward or outward.
It is a general phenomenon, not a handpan speciality. A guitar body and its sound hole form a Helmholtz resonator, typically tuned near the second lowest string. Car cabins do it when you open one window at speed. Bass reflex loudspeaker ports are deliberate Helmholtz resonators.
See also: PHY-10
PHY-10How does the gu port create the deep bass whoosh?#
beginner
Short answer. Any energy you put into the instrument shakes the enclosed air, and the cavity answers at its Helmholtz frequency, which on most handpans sits somewhere between roughly C2 and G2. That is well below every tuned note, so it reads as a bass undertone rather than as a pitch you played.Strike a tone field and it does not only push air outward into the room. It also pushes air inward into the cavity. That inward push is a broadband impulse, and it contains energy at every frequency, including the cavity’s own. The cavity picks out its resonance from that impulse and rings on it, driving the plug of air in the port in and out. Because the port is a large, well coupled opening firing into the room, the resulting low frequency radiates efficiently despite being a small share of the total energy.
The measured figures are consistent across makers, with the expected variation. PANArt found the Hang’s cavity resonance at about 85 Hz, which is close to F2, and stated that it could be detected in all spectrums of the instrument’s sound. Saraz report a general handpan range of about C2 to G2, with their own instruments typically landing between E flat 2 and F2 depending on shell size and port design. Since it varies with cavity volume and port geometry, expect any given instrument to sit somewhere in that band rather than at a fixed value.
Two things follow from this that players notice quickly.
It is always there. You do not have to do anything to hear the whoosh. It sits under every note as a warmth and a body that the instrument would sound thin without. This is a big part of why a handpan sounds much larger than its physical size.
It moves. Anything that changes the effective port area or neck length changes it. Resting the instrument on your thighs partly covers the port and lowers it. Sitting it flat on the floor obstructs it more. Lifting it clear raises it and lets it project. Makers exploit this too: covering the port or adjusting leg position is a standard way of bending the gu tone during play.
PHY-11What is the gu tone and how do I play it?#
intermediate
Short answer. The gu tone is the Helmholtz resonance played deliberately, by striking or slapping over the port with an open hand so that you drive the air plug directly. It is a deep, dry, bass thump, and bending it by opening and closing your hand over the port is one of the standard expressive techniques on the instrument.Playing a tone field excites the cavity indirectly. Playing the gu excites it directly: you use your hand as a piston at the mouth of the port.
The basic technique is to reach under the instrument, or tilt it, and strike the area around and over the gu with a relaxed cupped or flat hand. Aim for a slap that momentarily seals and then releases, rather than a hard hit on the steel. The steel around the port is not tuned and hitting it firmly does nothing useful; the sound you want is the air moving.
Variations worth practising:
- Open slap. Hand strikes and leaves immediately. Gives the fullest, most open gu tone at its natural frequency.
- Closed or muted slap. Hand strikes and stays, partly covering the port. Lengthens the effective neck and shrinks the effective opening, so the pitch drops and the decay shortens. This is the classic bass bend.
- Continuous modulation. Hover a hand over the port and move it while notes ring on the top shell. Because the Helmholtz resonance is present in everything you play, moving your hand sweeps the low end of the whole instrument. It is subtle, and it is very effective in a recording.
- Knee and leg control. How you sit changes the port coverage continuously and without occupying a hand. Many players use this without ever thinking about it.
PANArt built explicit variations on this idea. On the Integral Hang, partially blocking the gu produced a sympathetic D2. Their later Gubal replaced the central ding with a hand wide inwardly curved opening and made the deep cavity tone a primary voice, with a gung bass note at roughly 78 Hz, close to E flat 2.
The main practical caution is ergonomic rather than acoustic. Reaching under a four kilogram instrument on your lap for extended periods is awkward, and playing the gu is much easier on a stand or with the instrument tilted on one thigh.
See also: PLA section
PHY-12How does the air cavity couple the two shells?#
advanced
Short answer. The enclosed air is a shared spring touching the inside of both shells at once. Vibration of the top shell compresses it, and that compression pushes on the bottom shell, and vice versa. The two shells are therefore not independent: they are two plates joined at the rim and coupled through the air between them, and they behave as one system.There are two coupling paths between the shells and it is worth separating them.
The structural path is the rim. Bending waves in the top shell can in principle travel round the flange into the bottom shell. In practice this path is deliberately weak, because the rim is stiff, massive and damped by the adhesive joint. That is by design; see ANA-07.
The air path is the one that matters. Because the cavity is enclosed, any inward motion of one shell raises the internal pressure everywhere in the cavity almost instantly at low frequencies, and that pressure acts on every internal surface, including the whole of the other shell. Below the first standing wave frequency of the cavity, the air behaves as a single lumped spring and the coupling is essentially uniform.
The consequences:
The bottom shell is part of the instrument even though nothing is tuned on it. It is a large, relatively compliant plate that the cavity air drives. It radiates, and it stores and returns energy. Instruments with bottom notes make this explicit, but it is true even of a plain gu shell.
The cavity loads every tone field. A tone field pushing inward against an air spring behaves slightly differently from one radiating into free air. This is why sealing the port entirely raises the pitch of the notes and kills their sustain: the cavity becomes a stiff sealed spring with nowhere for the air to go.
Damping one shell damps both. Anything that touches the bottom shell, your legs, a cushion, the floor, adds mass and damping to a component that the whole system leans on. This is a real and audible effect, not a marginal one.
Above the frequency where the cavity’s own dimensions start to matter, the lumped spring model breaks down and standing waves take over. See PHY-13 and PHY-14.
PHY-13Why is a handpan louder when I lift it off my lap?#
intermediate
Short answer. Because your legs are doing two things at once: damping the bottom shell, which is an active radiating part of the instrument, and partly blocking the gu port, which is the main route by which low frequency energy escapes into the room. Lift it clear and you remove both restrictions.Take the two separately.
Damping. Flesh is an excellent absorber. Where your thighs contact the bottom shell they add mass and, more importantly, convert vibration into heat rather than reflecting it. Since the cavity air couples the bottom shell to everything else, damping it removes energy from the whole system, not just from the part you are touching. Notes get quieter and shorter, and the loss is concentrated in the low end where the bottom shell is most active.
Port obstruction. Your legs, and often a cushion or a strap, partly cover the gu. That does two things. It reduces the effective opening area, which lowers the Helmholtz frequency, and it restricts the airflow, which reduces how much bass energy actually reaches the room. Together they make the instrument sound smaller and duller.
This is why the same instrument can seem transformed on a stand. A good stand contacts the rim, which is already acoustically dead, and leaves the whole bottom shell and the port free. Players comparing instruments in a shop should insist on hearing them the same way, because lap versus stand makes a bigger difference than many of the differences they are trying to judge.
Some practical corollaries:
- If you play on your lap, a thin foam ring or a proper lap cushion that supports the rim rather than the dome preserves much more of the sound than resting the shell directly on your thighs.
- Sitting the instrument flat on a hard floor is the worst case: near total port obstruction plus a large damped contact area.
- Conversely, lap damping is a legitimate expressive tool. Lifting one thigh during a phrase opens the instrument up audibly, and some players use exactly that.
None of this is unique to handpans. Guitarists notice the same thing when a body is pressed against a chest, and the mechanism is the same: the resonator needs to be free to move and the port needs to be free to breathe.
See also: PHY-12, REC section
PHY-14How do shell geometry, standing waves and crossover shape the sound?#
advanced
Short answer. Above the Helmholtz region the air in the cavity supports standing waves whose frequencies are set by the internal dimensions, and the shells themselves have whole body bending modes. Where a tuned note lands close to one of these, the two interfere and the note develops an audible wobble in its sustain. Players and makers call that crossover or wave interference.The Helmholtz resonance treats the cavity air as one lumped spring, which is a good model only at low frequencies. Higher up, sound waves travelling across the cavity begin to reflect off the internal surfaces and reinforce or cancel at particular frequencies determined by the path lengths. Since path lengths are fixed by shell diameter and depth, so are those frequencies.
Saraz have published the most concrete measurements available and they map cleanly onto that model. Their primary interference band, described as the most intense and extending over roughly 150 cents, tracks shell diameter directly:
| Shell diameter | Worst affected note | Also affected |
|---|---|---|
| 19 in (48.3 cm) | C5 | B4 |
| 20 in (50.8 cm) | B4 | B flat 4 |
| 21 in (53.3 cm) | B flat 4 | A4 |
Larger shell, lower affected note, exactly as longer path lengths predict. They also identify a secondary, much subtler band producing 3 to 12 cents of instability, again shifting with diameter.
On their 21 inch instruments they describe B flat 4 as the worst case in their range: no matter how well the note is tuned, there is typically 20 to 50 cents of wobble in the sustain, particularly when it is the fundamental of a note. That is a large number, and the honest conclusion is that it is a geometric property of the instrument, not a tuning fault.
Temperature and humidity shift these frequencies because they change the speed of sound. Saraz note that A4 on a 21 inch chamber sounds good at around 27 degrees Celsius but becomes problematic below about 16.
What makers do about it: build several shell diameters so a problem note can be moved to a different shell, avoid offering scales that put an important note in the worst band, and experiment with internal baffling. Saraz report that closed cell foam and neoprene reflect rather than absorb and are modestly effective at particular positions, but rarely eliminate the interference.
Going deeper: the rim and the dome. The two pieces of geometry that are not tone fields do more than hold the instrument together. The rim is deliberately stiff, massive and damped by its adhesive joint, which makes it an acoustic termination: bending waves arriving there meet a large impedance mismatch and are absorbed rather than reflected back into the shell as whole-instrument modes. It also seals the cavity, which is the precondition for any Helmholtz behaviour at all, and its diameter fixes the internal path lengths that put the crossover bands where the table above shows them. The dome, meaning the overall convex curvature of each shell, is what makes thin sheet stiff. A curved plate resists bending far more than a flat one of the same thickness, which is what lets a 1 mm shell hold a tuned note without flopping. Curvature also varies across the shell, falling away sharply near the rim, and that gradient is part of why tone fields cannot be placed in the outermost band and why the fields nearest the rim behave differently from those near the ding. Locally, the small dome or dimple at the centre of each tone field applies the same principle at small scale: PANArt called their version dome embossment, discovered in 1997, and described the resulting saddle form prestress as the Rohner and Schärer buckling. It stiffens the middle of the field, sets its boundary conditions and suppresses some harsh high modes.