Acoustic Data

Here you will find acoustical information relevant to InfraSonic Experimentation.

Basics:

One of the more sobering facts one encounters when investigating the parameters associated with sound and electronics is the incredible sensitivity of the human ear.  The faintest sound at say 1000Hz produces a longitudinal displacement of about 10^-11 m !!!   Considering the wavelength of yellow light is about 6x10^-7 m, and the diameter of a molecule is in the order 10^-10 m, it can be seen that the ear is a remarkable piece of engineering!!   For this reason you have to work hard to make electronics 'hear' at a distance that the ear is quite comfortable with.   Of course, below 20Hz electronics has a better chance of being superior.

Speed of Sound:

Approximately 344 m/sec (1130 ft/sec) in air at 20^oC - varies with pressure, temperature and humidity.   To get a handle of this, a sound of frequency of 344Hz has a wavelength of 1m, or a sound of frequency of 1130Hz has a wavelength of 1 foot.

Attenuation:

The decrease in intensity of of a spherical wavefront sound wave is known as the inverse square law.   This accounts for a 6dB drop in intensity for each doubling in distance.  Further attenuation at ground level can account for, typically, up to another 6dB for each doubling of distance.

Absorption accounts for further losses, through direct conversion of the wave energy into heat.

Resonators:

Resonators are usually characterised by standing waves.   In the standing wave the node is where there is no movement of air, and an anti-node is where the movement of air is at a maximum.   This governs the relationship of standing waves to the enclosing resonator volume.

Open Tubes - the lowest possible frequency standing wave is where there is an anti-node at each end of the tube with a node in the centre.  Therefore the tube is one-half wavelength in length.   The lowest resonance frequency is:-

f = v/(2*L)

where v = velocity of sound and L = length of tube (both in the same units). All harmonics are supported.

Closed Tubes - here there is a node at the closed end and an anti-node at the open end.  The tube is then a quarter wavelength where:-

f = v/(4*L)

where v = velocity of sound and L = length of tube (both in the same units). Only odd harmonics are supported.

Helmholtz Resonator:

This resonator has just one resonance frequency with no other resonances below about 10 times the fundamental unlike the open and closed tubes discussed above.  Instead of analysing its behaviour from the viewpoint of standing waves, the Helmholtz resonator is analysed from the viewpoint of a mass suspended on a spring and exhibits simple harmonic motion.  This is why blowing across a small bottle produces a lower frequency tone than would be expected from calculations using standing waves.

Essentially, the enclosed volume is the spring while the plug of air in the neck of the vessel is the mass.

where c = velocity of sound, S = surface area of the neck, L = effective length of the neck and V = volume of main body.    Effective length is the actual length of the neck plus an end correction of about 1.5 times the radius of the neck.

For example, a cube box of internal dimensions 0.5, x 0.5m x 0.5m = 0.125m³, with a 90mm diameter pipe attached of length 1 m, will resonate at about 12Hz.