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Sonic crystals

2D finite difference time domain (FDTD) acoustics animations of a sonic crystal.

Below the first band gap

These animations show a (pseudo) plane wave sine pulse incident upon 10 periodically spaced layers of a sonic crystal. The radius of the cylinders is set to one-third of the cylinder spacing.

Below the first band gap sound is able to pass through (with reflections off the front & back due to abrupt changes in impedance).

Sonic crystal at 0.5 x f0

First band gap

At the band gap frequency, when half a wavelength fits in to layer spacing (for normal incidence), much lower levels of sound get through. A strong reflection back to the source is seen, and some sound appears to get trapped in the array.

Sonic crystal at 1.0 x f0

Above the first band gap

Above (1.5 x) the band gap frequency, sound is transmitted again, like at low frequency. Note how the sound travelling through appears to slow down inside the array before reemerging again at the speed of sound in free space.

Sonic crystal at 1.5 x f0

Second band gap

At twice the first band gap frequency the sonic crystal again attenuates much of the incident sound, letting very little through. At this frequency wavelength is equal to layer spacing, causing coherent back-scattering off the layers.

Sonic crystal at 2.0 x f0

Graded index arrays

At low frequency a sonic crystal is essentially a metamaterial, and by e.g. varying the size of the cylinders can be manipulated to have a variety of characteristics. In the following example, imagine the array being a side cross-section of a barrier rather than a view from overhead. This example shows a graded index array, which causes upward refraction by changing the refractive index and effectively slowing down the the incident wave progressively more with height due to the higher impedance (and essentially tortuosity) of the array towards the top. In the far-field, this can be used to create a shadow behind the array at frequencies below the band gap.

Note: this array has also been graded in the horizontal direction to minimise reflections off the front/back caused by abrupt change (discontinuity) in impedance.

Sonic crystal - graded index

As well as the above, graded index arrays have been investigated for applications such as acoustic lenses, acoustic black holes and acoustic cloaking.

Further info

Modelled using pyFDTD many of the features of which can be used interactively at FDTD Animate.

Based on original Twitter post here.

A combined YouTube video can also be found here.