Guitar resonance and soundhole geometry – Part 3: MY SOUNDHOLE EXPERIMENTS

PART 3: THE SOUNDHOLE EXPERIMENTS

This is the third in a series of nine posts summarising the results of an experiment I carried out during 2017 and 2018 to try to increase my understanding of resonance in acoustic guitars, and in particular how the design of soundholes could be improved.

This section describes the technical aspects of my experiments, and can be skipped by readers not interested in this.

The questions I ask in these experiments on guitar soundhole performance are:

o   Are there differences in the way a resonant cavity responds to the same stimulating signal when the soundhole size is changed?

o   What part does Helmholtz resonance actually play in the sound radiating from a guitar soundhole? Can soundhole area be used to control Helmholtz frequencies?

o   What is the source of the sound that radiates from the soundhole of a guitar?

o   Do soundslots (holes with a high perimeter to area ratio) perform better than round soundholes of the same area?

o   If slots are preferable to round holes, as the Royal Society paprer claims (see Part 1), designing a single long and narrow soundslot with area equivalent to the traditional 50mm radius soundhole is difficult without compromising soundboard strength. Is there any disadvantage in dividing the slot into two segments?

o   How well do experimental results derived from a rigid cavity translate to a real, elastic guitar soundbox?


THE EXPERIMENTAL RESONANT CAVITY

The experimental method uses a cavity made from sheet polycarbonate bent around the mould used for my Parlour guitar design. This cavity sits inside an outer box with the gap filled with sand to help damp out any vibration, since I am interested only in the response of the air-cavity as it is shaped by the soundhole. The sides and bottom of the containment box are 16mm MDF.


Figure 1: The rigid-walled resonant cavity

In operation the lower bout is topped with 12mm thick plywood, which has a speaker mounted in a box at roughly the position of the bridge. The upper bout is removable, and the square hole allows different size “soundholes” to be fitted and changed. This upper bout is held in place with thumbscrews to help damp out vibration, and heavy lead masses further restrict any vibrational response.

Figure 2: Resonant cavity with top and speaker box fitted

The next picture shows the operating setup. The lead weights (1.3kg each) are there to damp out any resonant response from the speaker box and cavity containment, allowing only the airbody to respond to the input signal. You can see one of the test soundholes in place – in practice I tried to overlap the corners of each soundhole with the lead weights.

Figure 3: Lead weights used to damp vibration in the top and the speakerbox – note the drop-in soundhole.

THE ACOUSTIC HOOD

This setup is placed inside a hood lined with acoustic foam to minimize room resonances that might otherwise affect the results. [1]

Figure 4: Ready to record (the near side of the hood has been removed for clarity)

You can see the microphone at the top of the sound hood

ESTABLISHING A BASELINE FOR SOUNDHOLE RESPONSE

The first reading for each measurement run begins with the hole blocked completely to establish a baseline, then “opening up” holes and measuring the change in response of the system relative to the closed box. The closed box signal is subtracted from the signal recorded for each soundhole.

Using the closed box signal as the measurement baseline also subtracts out the effect of any direct transmission of sound from the speaker box to the microphone.

CHIRP SIGNAL USED TO EXCITE THE CAVITY

The signal used to excite the airbody is a “chirp” generated by the software package Audacity. This is like a rising siren note starting on 50Hz and ending on 1000Hz. It is a pure sine wave signal with a 60 second duration, fed into the box from an iPod Classic through a small power amplifier. (Speaker and amplifier details can be found in Appendix 3)[2]

Audio file 1: The chirp signal used to excite the airbody

As you play this audio file, you may notice that your speaker or headphones respond better at some frequencies than others, so the sound seems to vary in level as it goes up the slide.

This is one of the problems in doing my experiment, because of course the speaker I used was just as incapable of reproducing the signal accurately at all frequencies as any other. No speaker I know of has an absolutely flat frequency response.

This is the reason why my experiment design relies on the closed soundbox signal as its baseline. The microphone at the top of the sound hood will pick up the signal from the soundbox, but also the signal that goes directly to the microphone from the speaker box. This “closed box” signal is subtracted from every open sound hole’s response, so that the final data set shows how much above or below the baseline signal the soundhole response is. This goes a long way towards erasing the speaker response as a component in the experiment.

The downside to this approach is that each sound hole’s response is relative, and can only be used comparatively – but that’s okay, because it’s comparisons I’m interested in.

DETECTING AND RECORDING THE SIGNAL

The soundbox response is picked up 80cm above the soundhole by a digital microphone (see Appendix 3) linked to a MacBook computer. Audacity is used to record the response signal at a sampling rate of 96kHz.[3]

Each run is repeated three times and the average used in analysis. 

Each run starts by recording the background noise for 5 seconds, followed by 60 seconds of soundhole signal.

Air temperature and relative humidity are noted because it is important to calculate the speed of sound for predicting the Helmholtz resonance response.

ANALYSING THE SIGNAL

Next, Audacity does a fast Fourier transform (Analyse / Plot spectrum) to produce a spectrum of the radiated sound. This is exported at a 1.5Hz resolution text file for each run, which can then be imported into Excel for analysis and graphing. 

Figure 5: typical soundhole response (Audacity Analyse/Plot spectrum function)

Once the data is in Excel, it is analysed this way:

  • Data sets (initially 0 to 30kHz) are trimmed to cover the range 0 to 5kHz. This culling of data makes it easier for Excel to operate, and there is little if any radiated signal above 2kHz anyway.
  • Because it is digitally recorded, the sound levels are in deciBels (dB), and are negative values. This is because digital recorders are often used for producing music, and aim to avoid digital clipping. They set 0dB as their upper limit.
  • The three sets of response data for each run are averaged.
  • The minimum level each averaged data set is subtracted at each measured frequency – this converts the readings to equivalently spaced positive dB values. But of course also disqualifies the data from any claim to being absolute. Relative readings are okay in this experiment because I am only interested in comparing soundhole responses to see if slots perform better than round holes.
  • The positive levels (β) are then converted from dB levels into radiated power readings in W/m2 so they can be added and subtracted validly   (II010(β/10))
  • Because the closed box response is the baseline (it also contains speaker response information and any direct transmission of sound from the speaker box to the microphone), it is subtracted from each data set to show the response of each hole or slot relative to each other and the closed box.
  • An analogue for total radiated power (again relative to the closed box) is found by adding up the radiated power calculated for each soundhole for each frequency band (resolution is 1.46Hz), essentially an integration across the spectrum.

After this analysis it is possible to plot graphs showing:

  • The spectral response of each soundhole
  • The total radiated power (relative to the closed box) across the spectrum, or any section of it, for each soundhole

This allowed me to understand the overall effectiveness of each soundhole as a radiator, and the tonal qualities of the radiation.

The disadvantage of the method is that it is not possible to say anything about the absolute values for radiated sound power.


SUMMARY OF PART 3

  • I am unaware of any experimental data describing the performance of guitar soundholes, so I set out to make my own measurements
  • The method used a rigid-sided guitar shaped air cavity with a “chirp” signal pumped into it to measure the resonant response of the airbody/soundhole combination across a range of frequencies
  • I changed the soundhole size and shape using a set of “drop-in” holes
  • The first experiment looked at the performance of round soundholes to establish some basic information (see Part 4) about how the sound projected varied with the size of hole
  • The motive is to discover if the traditional round guitar soundhole is the best design, or whether other shapes might offer better performance

WHAT’S NEXT?

In Part 4 we move on to analyse the response of round soundholes of different sizes, to establish a baseline on the way to finding out if soundholes of other shapes can outperform them. We’ll look at both the relative loudness of different sized holes, and also at the quality of the reproduction of the input signal≥


[1]See Appendix 4for an evaluation of the effectiveness of the hood – it certainly removed some room resonances.

[2]The speaker response is rated at 70Hz to 7kHz. In practice the signal was easily audible at below 50 to 70Hz, so the low activity of the resonator in this range is most likely a real measurement. (That statement hints at the limitations of the low-tech equipment used in these experiments…)

[3] If needed, Audacitycan subtract the background noise from the signal (Effects / Noise removal), so a new version of each data file can be saved after doing this, keeping the raw data as well. Trials showed that this made little difference to the results, so was not used.

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