Mech3200 Vibrations - Cymbal Vibration Practical

Cymbal Vibrations

Abstract Introduction

The aim of this demonstration project was to demonstrate the vibrations of a non-linear vibrating instrument, such as a cymbal, although seemingly erratic and impossible to analyse, can in fact be linked to the geometry and initial conditions of the cymbal.  

All cymbals are basically made of the same material. This is not quite true but is a good approximation, especially of high end cymbals, which are generally composed of 80% copper and 20%tin. A big thick cymbal will obviously be louder, as more air is moved by the metal, and will take longer to quieten down. A smaller, thinner cymbal will have lower volume, take less time to “open up” and has quicker decay.

We must also recognize that these particular cymbals do not have a specific “pitch”. The sound we hear is a mixture of a wide range of frequencies. Cymbals can, however, be characterized by the range of frequencies that dominate its response; this range is referred to as the “tessitura”. This concept can be clearly heard when two cymbals of the same size and shape, but of slightly different thicknesses are struck.  “As you can hear, there is no specific “pitch”, but an overall “range” which defines the sound.”

Theory

These cantilever equations show that for a given material and beam length, a thicker beam, even though the mass is higher, will have a higher stiffness and therefore higher natural frequency.  Cymbals in some ways are analogous to cantilever beam and in the same way a longer beam of the same thickness and material will have a lower natural frequency than a shorter beam, a bigger diameter cymbal of the same thickness and shape will have a lower tessitura then a smaller diameter cymbal of the same thickness and shape.

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[pic 2]

Apparatus

• Video Camera
• Monkey suit
• Tv
• Banana
• Computer
• Cymbal/s
• Drumstick

Procedure

Experimental Results

Mode shapes:

By modelling the vibrations and examining the fundamental modes of a particular cymbal (as shown in Appendix), it can be seen these mode shapes are significantly similar to those produced by a flat plate.  

Discussion

As can be seen from the results, the mode shapes of a particular cymbal can be compared to the mode shapes of that of a flat plate.  The frequency of each mode shape will change with size and shape, but the initial conditions also affect which mode will dominate the response and this can be seen from the results.  The video results show the tessitura which is compromised by a number of frequencies however they aren’t shown in the video but can be seen later on.  The tessitura of the cymbal can also be seen to be linked to the geometry of the cymbal and hence the bigger the diameter, the smaller the overall tessitura.