ARCHIVES OF ACOUSTICS
32, 3, 551–560 (2007)
MODES OF VIBRATION AND SOUND RADIATION FROM THE HANG
Andrew MORRISON(1), Thomas ROSSING(2)
(1)Illinois Wesleyan University
(received May 16, 2007; accepted August 13, 2007)
The HANG is a new hand-played steel instrument developed by PANArt in Switzerland.
We describe the modes of vibration, observed by holographic interferometry and the sound
radiation from the instrument observed by measuring the sound intensity in an anechoic room
by the two-microphone method. A low-voice HANG is compared with a high-voice HANG.
Keywords: HANG, sound intensity, steel instrument.
The steel pan or steel drum originated after World War II when the British and
American navies left thousands of 55-gallon oil barrels on the beaches of Trinidad.
Originally a rhythmic instrument, local musicians discovered how to transform the steel
pan into a melodious instrument by conditioning the metal and dividing the playing
surface into note area that could be tuned. Steel bands are now found all over the World,
especially in the Caribbean countries, North America, and Europe.
Steel pans, known by such names as tenor, double tenor, double second, guitar, cello,
quadrophonics, and bass, cover a range of more than 5 octaves. The end of the drum is
hammered (“sunk”) into a shallow concave well, which forms the playing surface, after
which the note areas are grooved with a metal punch. They are generally played with
sticks wrapped with rubber. Most of the note areas sound at least 3 harmonic partials,
tuned by skillful hammering .
In 2000, PanArt created a new hand-played steel instrument, which they called the
HANG. It consists of two spherical shells, fastened together. Like the pang instruments,
it uses nitrided steel. It quickly became very popular with percussionists, who learned
to create a wide variety of sounds. In this paper, we will discuss the acoustics of this
552 A. MORRISON, T. ROSSING
2. The HANG
The HANG is shown in Figure 1. The top (DING) side has 7 to 9 harmonically-
tuned notes around a central deep note, which couples strongly to the cavity (Helmholtz)
resonance of the body. The HANG is usually played in the lap, although it can also be
mounted on a stand. The bottom side has a large hole (GU) which acts as the neck of the
Helmholtz resonator. The resonator can be tuned by inserting a wooden collar (DUM)
into the hole, thus changing its diameter and neck length, or by varying the spacing of
the player’s knees to change the acoustical “length” of the neck. A wide variety of bass
tones can be achieved.
Fig. 1. The HANG (DING side and GU side).
The HANG can be tuned in a wide variety of scales. The high-voice HANG we
report in this paper had 9 notes tuned to a pentatonic scale, as shown in Fig. 2. This is
the same HANG describe in an earlier paper . Other scales are illustrated in Fig. 4.
The low-voice HANG had 9 notes tuned to an Ake Bono scale with the lowest note at F3.
Fig. 2. Tuning of high-voice HANG used in these studies.
MODES OF VIBRATION AND SOUND RADIATION FROM THE HANG 553
3. Modes of vibration
Each of the notes on the HANG has three tuned partials with frequencies in the ra-
tios of 1:2:3. Modal analysis can be done by several methods, but the ﬁnest resolution is
obtained using holographic interferometry. An electronic TV holographic interferome-
ter is shown in Fig. 3. The object beam is projected on the HANG, and the reﬂected light
is focused on the CCD array of a TV camera, while the reference beam is transmitted to
the camera by means of an optical ﬁber. The resulting interference pattern is read out,
pixel by pixel, and the holographic interferogram is constructed by a computer. Thus, an
interferogram is created and updated at the TV frame rate (30 Hz in the United States).
Figure 4 shows the high-voice HANG mounted on the air-supported optical table for
Fig. 3. Apparatus for electronic TV holography.
Five modes of vibration in the central G3 note area of the high-voice hang are illus-
trated by the interferogram in Fig. 5. In the (0,1) mode of lowest frequency, the entire
note area vibrates with the same phase, while in the (1,1)aand (1,1)bmodes a nodal
line bisects the note area. The nodal lines in the two latter modes are orthogonal to each
other, so they represent normal modes. These three modes at 189, 390, and 593 Hz have
frequencies nearly in the ratio of 1:2:3. Also shown in Fig. 7 are the (2,1)aand (2,1)b
modes having two nodal diameters and frequencies 1418 and 1543 Hz which are not
harmonically tuned. The three lowest modes in the E4 note area, shown in Fig. 6, also
have frequencies in the ratios 1:2:3, although the higher modes are quite different from
those seen in the G3 mode.
The holographic interferograms in Fig. 5 serve as contour maps of the vibration am-
plitude. The “bull’s eyes” represent the points of maximum amplitude, and each fringe
(light or dark) represents a decrease in amplitude equal to 1/4of a wavelength of the
laser light used (532 nm in this case). Information about relative phase is not recorded
except that adjacent areas generally differ in phase by 180◦. To recover phase data,
we modulate a second mirror with a signal at the drive frequency having an adjustable
phase. Then it is possible to obtain a phase map . Phase maps are useful in studying
coupling between note areas.
554 A. MORRISON, T. ROSSING
Fig. 4. High-voice HANG mounted on holographic table.
Fig. 5. Modes of vibration in the central G3 note area of the high-voice HANG.
MODES OF VIBRATION AND SOUND RADIATION FROM THE HANG 555
Figure 6 shows phase maps of the D4 note area vibrating at its second resonance
frequency (604 Hz) and the D6 note area vibrating at its lowest resonance frequency
(also 604 Hz).
Fig. 6. Phase maps of the D4 note (left) at its second resonance frequency (604 Hz) and the D5 note (right)
at its lowest resonance frequency (604 Hz).
Holographic interferograms of the low-voice HANG driven at small and large am-
plitude at frequencies near the ﬁrst three resonance frequencies of the central F3 note
are shown in Fig. 7. The mode shapes of the (0,1),(1,1)aand (1,1)btuned in the ratios
1:2:3 are similar to those shown in Fig. 7. The coupling between various notes can also
be seen. At 348 Hz, for example, the F4 note is strongly driven and the F4# is weakly
driven, while at 520 Hz the (1,1)amode in the C4 note and the (0,1) mode in the C5
note show appreciable response.
Fig. 7. Low-voice HANG driven at frequencies near the ﬁrst three resonances of the central F3 note. Upper
hologram at each frequency shows small driving amplitude, lower hologram shows large amplitude.
556 A. MORRISON, T. ROSSING
In Fig. 8 the low-voice HANG is driven near the ﬁrst three resonance frequencies of
the F4# note. The (0,1), (1,1)a, and (1,1)bmodes are shown, along with coupling to the
(1,1)amode of the C5# note.
Fig. 8. Low-voice HANG driven at frequencies near the ﬁrst three resonances of the F4# note. Upper
hologram at each frequency shows small driving amplitude, lower hologram shows large amplitude.
4. Sound intensity
A convenient way to describe the acoustic ﬁeld of a sound source is by accounting
for the ﬂow of acoustic energy outward from the source. The acoustic power density
through a surface is called the sound intensity I. Complete theoretical treatments of
sound intensity in monochromatic ﬁelds are widely available [3, 4]; only a brief sum-
mary is presented here for reference. The instantaneous intensity is the product of sound
pressure p(r,t) and acoustic velocity u(r,t):
I(r, t) = p(r, t)u(r, t).(1)
For a source vibrating at frequency ω, the instantaneous pressure is
p(r, t) = P(r) cos(ωt −ϕ(r)).(2)
The acoustic velocity is
u(r, t) = −1
where ρis the air density. Substituting (2) into (3) yields
u(r, t) = 1
ωρ P(r)∇ϕ(r)cos(ωt −ϕ(r)) −1
ωρ ∇P(r)sin(ωt −ϕ(r)).(4)
MODES OF VIBRATION AND SOUND RADIATION FROM THE HANG 557
The instantaneous intensity can be written:
p(r, t)u(r, t) = 1
ωρ P2(r)∇ϕ(r)cos2(ωt −ϕ(r))
ωρ P(r)sin(ωt −ϕ(r))cos(ωt −ϕ(r)).(5)
The sound intensity can be written as the sum of the active intensity (AI) and the
reactive intensity (RI), which are in quadrature: I(r, t) = A(r, t) + R(r, t). A(r, t) is
associated with the component of u(r, t) in phase with p. The time-averaged form of
the AI component is the power ﬂux, while RI represents power stored in the near ﬁeld.
A vector ﬁeld plot of AI shows vectors pointing in the direction of power ﬂow, while
RI vectors show the stored energy ﬂux close to the sound source. The RI component of
total intensity drops off as distance from the source increases, falling to zero in the far
Intensity measurements of the sound ﬁeld of the HANG were made in an anechoic
chamber. A frame of aluminum tubing was suspended from the ceiling to support the
instrument and the driving apparatus. An Ono Sokki CF-6410 sound intensity probe
and a CF-360 FFT analyzer were used to measure the sound intensity at various planes
near the HANG. The sound intensity probe consists of a pair of matched microphones
with a spacing of 7 cm between them. The probe and analyzer allow for simultaneous
acquisition of AI and RI. A good approximation to acoustic velocity is obtained from
the pressure difference between the microphones as they move in the sound ﬁeld.
Active intensity measurements in a plane 8 cm above the top (G3 bass note) of the
high-voice HANG are shown in Fig. 9. In the top row, the D4 note was excited by a
swept-sine signal (0≤f≤2000), and the intensity ﬁelds at the lowest three resonance
frequencies were mapped over a 10×10 grid with 7 cm spacing between adjacent points.
In the second row, the E4 note was similarly excited, while in the third row the A4 note
The active intensity maps show monopole radiation characteristics at the fundamen-
tal and second harmonic frequencies. The intensity ﬁeld at the fundamental frequency
exhibits a peak in AI directly over the note being driven. The intensity ﬁeld at the sec-
ond resonance frequency shows the largest active intensity region to be centered over
the instrument and distributed over a large portion of the instrument. The intensity ﬁeld
at the third resonance frequency exhibits a dipole pattern.
Reactive intensity measurements in the plane 8 cm above the HANG are shown in
Fig. 10. As in Fig. 9, the D4 (top row), E4 (middle row), and A4 (bottom row) notes
were excited over the frequency range of 0 to 2000 Hz. The reactive intensity ﬁelds
show a circulatory pattern at all three resonance frequencies. The RI shown is the peak
value per cycle. Half a period later, the vectors have reversed their direction. For the
three modes measured, the RI aligns mostly in a circulatory pattern which suggests an
exchange of energy between the front and back of the instrument.
558 A. MORRISON, T. ROSSING
Fig. 9. Active intensity plots in a plane above the top of the HANG at the ﬁrst three resonance frequencies
of various notes of the HANG: (a) D4, (b) E4, (c) A4.
MODES OF VIBRATION AND SOUND RADIATION FROM THE HANG 559
Fig. 10. Reactive intensity plots in a plane above the top of the HANG at the ﬁrst three resonance frequen-
cies of various notes of the HANG: (a) D4, (b) E4, (c) A4.
560 A. MORRISON, T. ROSSING
The HANG is a new hand-played steel instrument which has caught the fancy of
many percussionists worldwide. Through experimenting with playing technique, per-
formers have created many new sounds, and continue to do so. Understanding the modes
of vibration and the sound radiation from the instrument help them to do so, as well as
adding to our knowledge of the science of musical instruments.
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