These are the different shapes that a cymbal makes when it vibrates after you hit it, looking at the top of it. The white areas are where the cymbal doesn't move, is stationary, but it vibrates all around these areas up & down. For each picture all the vibrating areas have the same frequency. The pictures shown range in frequency from 40 Hz to 1135 Hz.
Each picture shows a pattern of motion that occurs at a specific frequency. Engineers call the shape patterns "modes". After the cymbal is struck, many of these different mode shapes happen at the same time, at their individual frequencies, so when you look at a vibrating cymbal it appears almost random in its motion, but the motion is really a sum of all of the different mode shapes vibrating simultaneously - see the animations at the end of this blog.
If you vibrate the cymbal with something like a speaker, and slowly increase the frequency, you will find that the mode frequencies are also the resonance frequencies of the cymbal. You will see and hear the amount vibration increase a lot as you reach each mode (resonance) frequency. This video shows a membrane being excited by a nearby speaker playing tones at some of the resonance frequencies, the membrane and speaker motion is made more visible due to the use of a strobe light which highlights the motion at longer intervals than you normally see (~20fps):
Circular Membrane (drum head) Vibration
Every physical object has this same thing happen. Every physical object has resonance frequencies, and a specific shape of vibration associated with each frequency. When a cymbal is struck, many of the resonances may be excited at once because of the impact. But most of the energy goes into the lower frequencies of vibration, and each higher frequency typically has less energy than the previous one. Also, the frequencies that are excited depend on where and how the object is impacted, this is why things sound different when you hit them differently. If you excite the object at a spot where the mode shape doesn't have a lot of natural motion, you will not excite that frequency very much, and vice-versa.
Interestingly, physics has been able to predict the mode frequencies of complicated objects and their shapes somewhat accurately. You actually only need to know 3 things: the material stiffness, material density, and the shape of the object, and it can be solved! Meaning you can calculate the mode frequencies and the mode shapes. Here are some good examples I found on YouTube of vibration prediction /analysis:
1. This animation shows the motion of one of the modes (a mode shape) of a circular membrane clamped around the edge:
Vibrating Circular Membrane Mode
2. This animation shows the first 4 modes of a circular membrane clamped around the edge. Notice as the mode frequency increases the vibration shape gets more complicated. With the assumptions of continuum mechanics (ignoring atomic-scale effects) there is no limit to how high the theoretical mode frequency can go, but you would eventually need to consider heat, electrodynamics, and quantum mechanical physics. For instance, visible light is the result of atomic vibrations near 500 TeraHz (500,000,000,000,000 Hz).
First 4 Vibration Modes of a Membrane
3. This animation is an representation of what might happen when the membrane is excited by an impact force, which distributes energy into many modes and so many mode shapes and frequencies occur simultaneously after. If you look carefully, you can recognize some of the individual modes. It appears complicated but physics says the motion is represented by the sum of many single modes:
Superposition of 25 Modes of Vibration on a Circular Membrane.
This motion would be similar to the actual cymbal motion as shown is this video by Meytal Cohen:
Meytal Cohen Cymbal Crash Slow-Mo
4. This type of prediction analysis is done routinely on every type of engineering structure where vibration is important! For instance, here is a vibration mode predicted for a spacecraft antenna:
Vibration Mode of a Spacecraft Antenna
Hope you learned from this!
steve
