Free plate frequencies

It is difficult to assess the relationship between the resonant frequencies of the free plates and the plates in an assembled violin. Some makers claim that free plate tuning is for that reason a waste of time. I think that using the following methods to measure the frequencies of the free plates as you are working on them can add to your understanding of how the sound system of the violin works. These methods are not a complete solution in themselves, but may help you produce, in time, better sounding instruments. With all these, you should keep a log for every violin you build so that you can refer back to it in case your instrument turns out to have an exceptionally good tone.

Chladni patterns

The free plates, when excited at certain frequencies, give exceptional responses. These responses can be visualized with the help of small particles. The vibrational response of the free plate can spatially be divided in areas with strong response {anti-nodes} and areas with with little response {nodes}. To get the strongest response possible, the plates should be fixed at points of as little vibration as possible {nodes} and should get excited in the area of anti-nodes.

Three frequency responses, or modes M1, M2 and M5 are considered important in violin plates although a number of other minor modes could be found.

See Fig. 1-3 for M1, M2 and M5 modes Chladni patterns. The red circle is where the driver {speaker} should be placed. The red rectangles denote the positions of foam patches which support the plate at the nodes.

The speaker is connected to a power amplifier, which is in turn driven by a sinus signal generator, ie a PC with tone generator software.

1. Set up the plate upside down supported by the foam patches, see red rectangles in Figs.
   
2. Place the speaker at the position of the red circle.
   
3. As the detecting particles use black tea powder extracted from a couple of tea bags.
   
4. Spread the tea powder evenly on the inner side of the plate.
   
5. Controlling the tone generator, start a frequency sweep from 400 Hz down. The speed of the sweep should be maybe 1 Hz per second so that you notice when the plate starts to resonate.
   
6. First you should reach the M5 frequency. See Fig. 2 for the M5 pattern.
   
7. When you see the M5 pattern form, that's the plate's mode 5 frequency.
   
   

The same applies for M2 and M1 modes. The M2 should be somewhere about half of M5 and M1 could be above half of M2. For best results make sure the speaker is at the sweet spot and so are the foam pads. The nodes should really have almost no vibrations at all while the rest should be vibrating strongly.

The patterns presented in Fig. 1-3 are for the back plate and top plate before f-holes are cut and bassbar added. The top plate with f-holes and bassbar installed generates slightly different patterns.

Application

So how is this helpful. First, the patterns should be in one word nice. Every plate is different and the wood varies in density but you should not have patterns that have gaps in them or are otherwise obviously a result of poor arching or wildly inconsistent wood.

Again, it is a visualization of the frequency response of the whole plate so if you happen to make a great violin it would be good to know how the patterns looked like.

Second, the patterns can help you locate mode frequencies you may otherwise have a hard time recognizing, either by ear or in software plots /more on both later/.

Measuring free plate modes by ear

The basic principle is the same here. The speaker is substituted by your knocking finger and the foam pads by your fingers. So you hold the plate at an anti-node, knock and listen for the dominant frequency response.

See Fig. 4 to learn where to hold the plates and where to knock. The top positioned "x" is the spot where you hold the plates, the lower positioned "x" marks the place where to knock.

Application

This serves as a quick method during plate graduation, when you need to keep track of how the modes keep changing based on where you remove wood.

For most people it is impossible, without any reference, to know what pitch in scale tones or Herz they are hearing. Here are some methods to reference what you are hearing:

1. Use a monochord. Knock and then tune the monochord to the pitch you are hearing to get the frequency.
   
2. Use a chromatic electronic tuner and whistle the pitch you are hearing.
   
   

Measuring free plate modes by microphone

The method is identical with the previously mentioned knocking so refer to Fig. 4 if you need to. Your ear is supplanted by a microphone and a computer software for analysis. This option will not only give you the the pitch of the mode but also a whole frequency "image" or plot of the plate. As this method seems to be the most commonly used today, we will describe it in some detail.

1. Download and install Audacity recording software.
   
2. Connect a microphone.
   
3. Hold the plate in front of the microphone and record a series of knockings.
   
4. In Audacity, highlight the sound wave or just the part of it you think is the most representative.
   
5. From top menu choose Analyze> Plot spectrum.
   
6. A windows shows up where you choose Size > 16384, Axis > Log frequency.
   
   

That's it. The plot you see, Fig. 5 is an example, is the graphical interpretation of the plate's frequency response. The mode you are holding and knocking the plate for should be the strongest spike in the spectrum. Again M5 should be somewhere between 300-400 Hz, M2 half of M5 and M1 above half of M2.

This works most of the time but sometimes, especially with M1 and M2 it can be quite difficult to locate. Chladni patterns can help you here.

Humidity

The plate frequencies are bound the the amount of water in the wood. Therefore, you should take your measurements in a stable environment. Humidity of about 47 percent can be considered ideal.