Introduction to Acoustics

noise source, which can be played over a very wide
range of intensities, from very soft to very loud, to
support, for example, a Rossini crescendo. Because
the side drum is designed to produce short percussive
sounds or a wide-band source of noise, little effort is
made to tune the partial frequencies of the two drum
heads.
Like the timpani and Indian drums, the vibrational
modes of the drumheads can be strongly perturbed in
frequency by the air coupling. When used as a snare
drum, the induced vibrations of the non-striking head
can be sufficient for it to rattle against a number of
metal cables tightly stretched a few mm above the
surface of the non-striking head. The resulting interruption
of the vibrations, on impact with the snares,
leads to the generation of additional high-frequency
noise and the sizzle effect of the sound excited.
A not dissimilar effect is used on the Indian tambura,
an Indian stringed instrument investigated by
Raman [15.210], which has a bridge purposely designed
to cause the strings to rattle Fletcher and Rossing ([15.5],
Fig. 9.30).
Figure 15.118 shows the waveform and timeaveraged
FFT of a side-drum roll (audio ). The
spectrum is lacking in spectral features other than a modest
peak in noise at around 100–200 Hz, associated with
the vibration of the lower head against the snares.
Although the exact placing of the vibrational modes
of the strike and snare heads are of little acoustic
importance, their coupling via the enclosed air illustrates
the general properties of double-headed drums
of all types. The first four coupled normal modes are
(dB)
0
–100
0 1 2 3 4 5 6 7 8
(kHz)
2 s
Fig. 15.118 Time-averaged FFT spectrum and waveform of
the sound of a snared side-drum roll of increasing intensity
Musical Acoustics 15.4 Percussion Instruments 647
shown in Fig. 15.119, which is based on data from Rossing
([15.211] Sect. 4.4). For a freely supported drum,
momentum has to be conserved, so that normal modes
with the two heads vibrating in the same phase will also
involve motion of the supporting shell of the drum, as
indicated by the arrows in Fig. 15.119.
As anticipated, the air coupling increases the separation
of the (01) modes from 227 and 299 Hz to 182 and
330 Hz, and the (11) modes from 284 and 331 Hz to 278
and 341 Hz. The perturbations in modal frequencies will
always be largest when the coupled modes have similar
frequencies. Such perturbations becomes progressively
weaker at higher frequencies, partly because the coupling
from the enclosed air modes becomes weaker and
partly because the frequencies of the two drum-head
modes having the same symmetry become more widely
separated. The higher modal frequencies are therefore
little different from those of the individual drum heads
in isolation.
Figure 15.119 also illustrates the anticipated polar
radiation patterns for the normal modes measured
by Zhao [15.209] and reproduced in Rossing ([15.201]
Figs. 4.7 and 4.8). The coupled (10) normal modes act
as a monopole radiation source, when the heads move in
opposite directions, and a dipole source, when vibrating
in anti-phase. In contrast, the (11) modes with heads vibrating
in phase act as a quadrupole source, and a dipole
source, when vibrating in anti-phase.
Dipole Quadrupole
(01) 227 182 Hz (11) 284 278 Hz
Monopole Dipole
(01) 299 330 Hz (11) 331 341 Hz
Fig. 15.119 Coupled motions of the two drumheads of a side
drum, indicating the change in frequency of the drumhead
modes from air coupling within the drum and the associated
polar radiation patterns (after Zhao et al. [15.209])
Part E 15.4