Air Loading

The air that comprises the earth’s atmosphere is made of many different gases. Nitrogen accounts for as much as 78% of the volume while Oxygen accounts for almost 21%. The remaining 1% is composed of such gases as Argon, Carbon Dioxide, Helium and Hydrogen. Water vapor (water in its gaseous state) is also present in the atmosphere in varying amounts, by up to 2%. This atmosphere can be thought of as large ocean of air surrounding the earth.

Air and consequently, our atmosphere, do have weight. The weight of the air is referred to as air density. This weight (air density) decreases as you go up within the atmosphere. When gravity acts on the air, the air exerts a force upon the earth called pressure. Air pressure varies according to temperature. Cold air is more dense than warm air, i.e., it weighs more. As a result, it tends to sink. Warm air, on the other hand, is less dense. Therefore, it weighs less and tends to rise. Meteorologists say that warm air is buoyant. ¹³

Unlike a vibrating string, which requires a carefully designed coupled surface to propagate its sound, a vibrating timpano heads strongly couples to the surrounding atmosphere, which in turn propagates the sound. Since air does have weight, air density plays an integral role in affecting how a timpano head vibrates. Compared to a vibrating string, a timpano head is considerably larger in size and the surrounding air mass (both inside and outside of the drum) interacts with the vibrating modes substantially. This phenomenon is called air loading and is the main factor responsible for establishing the near-harmonic relationship among the preferred modes. Air loading is the effect the weight of the surrounding mass of air has on the motion of the timpano head. It lowers the natural frequencies of vibrations from those of a ideal circular vibrating membrane. This effect is strongest for the lower modes especially mode (1,1), (2,1) and plays a significant role in the adjustment of the inharmonic partials. Since air density is not a constant, factors that affect air density (barometric pressure, temperature and humidity) also affect how a timpano head vibrates. The most noticeable effects are slight fluctuations in pitch and changes in the color of the sound when air density changes.

Thomas D. Rossing and his colleagues (Rossing et al., 1976, 1977, 1982, 1998, 2000) summarized the effects of air loading and membrane stiffness as follows: (membrane stiffness is a slight secondary influence on establishing “harmonicity” of the preferred modes) ¹⁴

1. 1. the air loading results in a considerable decrease in the frequency of the lower modes, but the loading is small in the modes of higher frequency
   2. the bending stiffness increase the frequency of the higher modes very slightly, but it is virtually ignorable for the membrane used for a kettledrum
   3. the stiffness to shear is considerable at large amplitude but the resulting forces are of second order and there fore may be considered small at ordinary playing amplitudes of a kettledrum

A crucial component to the production of harmonic timpani pitch is how the vibrating head interacts with the air above and below it. Equalizing the density of the volume of air inside the drum (i.e. air pressure, temperature and moisture content) to that of the density of the air above the head is integral. The interaction between the masses of air inside and outside of the drum contributes significantly to the actual pitch and perceived harmonicity of timpani. Ideally, these masses of air should always have the same density as when the heads were last tempered.

Both the vibrating head and the volume of air inside of the bowl have specific modes of vibration; the air masses inside and outside of the bowl influence how the head will vibrate based on the external air density and the volume and density of air contained within the bowl.

Preferred Modes (1,1)  (2,1) (3,1) (4,1) (5,1) of the vibrating head.⁴⁰

Vibrational modes (determined by volume)  of the air enclosed within the bowl ⁴¹

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