Metamaterial drum

One special feature of metamaterial is the cloaking behaviour. Here a wave entering a structure is not entering this structure. The wave behind the structure looks as if no structure was there. Therefore the inside of the structure is cloaked.

The frame drum below has been modified by adding magents in a circle. Below the drum with the magnets is shown. It is placed in front of a microphone array to record the drum head vibrations:

When striking the drum inside the circle (below figure, top), outside the circle (below figure, bottom), or at the circle rim (below figure, middle) the sound is considerably different. When striking inside a sound not known from regular drums is heard. When striking outside a normal drum sound is still there. And when striking at the rim a mixture of both is produced.

Where is the sound when striking the frame drum outside a magnet circle of 10 cm diameter:

When striking inside the circle:

When striking at the magenet ring:

The diameter decides about the width of the bandgap. The width is smaller for the same drum with a magnet ring of 8 cm, again outside:


and at magnet ring:

The bandgap gets wider with a diameter of 12 cm, again outside:


and at magnet ring:

The microphone array  shown above is recording the radiated sound, and a back-propagation algorithm determines how the drum vibrates at all frequencies up to 1 kHz. Then all positions, where the vibration has an amplitude maximum are summed up. When striking inside the circle nearly all mode maxima are in the circle (below figure, top). When striking outside the circle the maxima are all outside (bottom), and when striking at the circle boundary a mixture happens:

The reason is a frequency-dependent cloaking behaviour. Below are time frames of a strike inside the circle, recorded by a high-speed camera with a laser interferometry system. Some waves leave the circle, but much more stay inside:

The opposite happens when striking the drum outside the circle. Most waves are not able to enter the circle:


Still this is frequency-dependent. Driving the drum inside and outside with a low frequency (top) and a high frequency (bottom), the waves of the low frequency are able to enter, while those of the high frequency are not:

This leads to a band-gap in the spectrum between about 300/400 Hz and 700/800 Hz. Below are three figures, each have three spectra for three circles with diameters of 8, 10, and 12 cm. When stiking inside the circle (top figure) there is such a bandgap. Such a sound cannot be produced with a regular drum. When striking outside (bottom figure) a normal spectrum appears, indeed we hear a normal drum sound. The strike at the circle rim is again in between:

Therefore with a modified metamaterial drum, sounds can be produced not possible with normal drums. Still the normal drum sound is preserved and mixtures can be played, too.


Bader, R., Fischer, J. L., Münster, M. & Kontopidis, P.: Metamaterials in Musical Acoustics: A modified frame drum. JASA 145 (5), 3086-94, 2019.

Metamaterial String

Another classical example of a 1-dimensional metamaterial strig is that of a sonic crystal, where masses are attached to a string. When adjacent masses alter from smaller to larger mass, a dispersion relation of two brances is achieved. When using 74 masses on a string the theoretical dispersion relation as shown in the figure below on the lower left is achieved. Still in reality the system is much moe complex as shown in the time series (upper left), spectrum (upper right) and dispersion relation (lower left) in the experiment:

The sound of a Finite-Difference Time Domain (FDTD) model of such a string sounds like this:

While such a string, recorded by a piezo at the string end sound much more compex:

Lit.: Bader, R. & Kotopidis, P.: Acoustic Metamaterials for Sonically Designing Musical Instruments and Room Acoustics. In: Sonic Design. Springer Series Current Research in Systematic Musicology, 2023 (in print).