Trapped air in a drum bowl alters the head’s mode frequencies from ideal values

Evidence

The modes produced when a kettledrum is struck are the same shape as those given in Figure 4.31, but their mode frequencies are different from those of an unmounted head (shown as “ideal” in Table 4.2), because of the effect of the air in the bowl over which the head is stretched and the position at which it is struck. Hall (2001) describes this as follows: “When sections of the head move into and out of the bowl, other sections move in the opposite direction (out of and into the bowl respectively).” These are marked in Figure 4.31 with plus and minus signs. The (0,1) mode is an exception to this, and it is marked with “−/+” since it involves the whole head moving either into or out of the bowl, as it attempts to compress and rarefy the trapped air respectively. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1302

The modes produced when a kettledrum is struck are the same shape as those given in Figure 4.31, but their mode frequencies are different from those of an unmounted head (shown as “ideal” in Table 4.2), because of the effect of the air in the bowl over which the head is stretched and the position at which it is struck. Hall (2001) describes this as follows: “When sections of the head move into and out of the bowl, other sections move in the opposite direction (out of and into the bowl respectively).” These are marked in Figure 4.31 with plus and minus signs. The (0,1) mode is an exception to this, and it is marked with “2/1” since it involves the whole head moving either into or out of the bowl, as it attempts to compress and rarefy the trapped air respectively. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1325

Categorization

• QUESTION: How is the position of the strike supposed to alter mode frequencies beyond bowl air effects? Worth tracing how strike position interacts with bowl loading.
• XREF: Connects to the reader’s standing interest in how physical containers/cavities shape acoustic resonance — parallels earlier discussion about why a resonance box (guitar body) raises the loudness of certain strings. — connects to: Body-volume changes drive the Helmholtz air mode in stringed instruments — Eric J. Heller, Why You Hear What You Hear- An…, 1794; The kettledrum bowl lowers its head modes toward harmonic ratios; The bowl’s trapped air shifts kettledrum mode frequencies from ideal values.
• DEFINE: Explains the plus/minus mode-coupling mechanism of air loading and the (0,1) ‘2/1’ exception that compresses the whole trapped air volume.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1302; David Howard, Jamie Angus, coustics and Psychoacoustics, 1325

Broader Connections

• The bowl’s trapped air shifts kettledrum mode frequencies from ideal values. #corroborates (0.98)
• The kettledrum bowl lowers its head modes toward harmonic ratios #complicates (0.72)
• Body-volume changes drive the Helmholtz air mode in stringed instruments #expands (0.70) — Eric J. Heller, Why You Hear What You Hear- An…, 1794