Orbital Sound

Theory

If both ends of a tube in a musical instrument are uncovered its an open end air column. E.g. woodwind instrument

The resonant frequency depends on the dimensions of the air column in conjunction with the air speed and temperature.

Anti-nodes or maximum vibration exist at the open ends of the air column with the length of the air-column half the wavelength of the fundamental frequency.

The frequency would be calculated as f =V/2L = 343.7 m/s /(2*0.012 m) = ~14.32kHz

However, being a sphere its a more complex process.

If we cover one hole the sphere approximates to a Helmholtz Resonator without a neck.

With calculated frequency of 72.6*SQRT(0.002/(0.012^3)) = ~2.47kHz

Both frequencies are within the audible range of 20Hz to 20kHz although there are variation between individuals particularly at the higher end.

However, the spinner is not travelling at a constant speed but accelerating and decelerating thus affecting the intensity and frequency of the sound.

Additionally, multiple harmonics are also produced at higher frequencies than the fundamental.

For the design spheres rather than cylinders are used as they offer better stability in motion offering less air resistance and being more streamline..

When the spinner is turning air passes quickly over the outer surface creating a pressure difference attempting to pull air out of the sphere conversely the lower pressure created attempts the suck the air back in.

These oscillations of the air repeat at long as the spinner rotates.

Design

The device will be required to rotate rapidly without the use of batteries or electrical motors.

This will be accomplished with the energy stored in a wound string with an offset axis.

In order for the device to rotate smoothly it is required to be balanced and symmetrical, a circular object fits the bill.

The circular object will normally rotate in the vertical plane.

As this device was to be 3D printed consideration needs to be given to the overall shape, size, strength and aerodynamics.

The circular object comprises a supporting dual hoop wheel with 4 spokes and a central hole.

But this on its own is not what will make the sound we desire.

In order to make the noise we require some resonators.

The resonators will be hollow spheres with two holes, one at each of horizontally opposite aligned poles.

A total of four resonators will be included which will fit between the gap of the two spokes.

Two small oppositely placed rings will be placed close to the centre through which the string will be laced.

In order to negate the requirement for supports and ensure the spheres are hollow.

The device (spinner), will be created in two halves in order to print it flat and then the two halves will be stuck together.

Printing in two halves enables the spheres to be inspected internally for issues.

Design details:

Radius of the outer hoop is 32 mm

Radius of the inner hoop is 18 mm

Radius of the spheres is 7 mm with wall thickness 1 mm.

Radius of the holes in the spheres is 1 mm.

Spokes and hoop thickness is 2 mm.

Print Settings

Layer Height - 0.15 mm

Infill - Tri-Hexagon

Infill Density - 50%

Base Adhesion - Brim

No supports.

Filament - PLA

Weight - 9 grams

Print Time - 1 hour 22 mins

Full details can be found at: Orbital Sound : 7 Steps (with Pictures) - Instructables