PART 4: HOW THE SIZE OF A SOUNDHOLE DETERMINES THE WAY A GUITAR AIRBODY EMITS LOW FREQUENCY SOUND FROM 90 TO 1000Hz (E1to E6)
This is the fourth 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 tests the properties of the traditional round guitar soundhole shape.
The central question here is how the radius of a guitar soundhole affects the loudness and tone of the sound that comes from the soundhole of a guitar.
As I show later in Part 6, airbody resonance is only one source of the sound that emerges from a guitar soundhole.
Part 3 discusses the experimental method in detail.
Figure 1 below shows the resonant cavity used in the experiment. It is the size and shape of one of my Parlour size instruments.
A stiff heavy top was added, including a box for a small speaker in the lower bout and a hole for the drop-in soundholes in the upper.
Figure 1: A view of the resonant cavity used in the experiment
Figure 2: The cavity with the top added – the box contains the speaker used to excite the cavity, and you can see where the different-sized drop in soundholes go
A digital microphone captured the sound coming from each hole for analysis. An acoustic hood was used to damp out stray resonances from the room (see Appendix 4 for an evaluation of its effectiveness).
Figure 3: the experimental setup showing two out of three sides of the acoustic hood
Lead weights were used to further damp any vibrational response in the cavity top and speaker box.
The method I used was:
- The stimulating signal was a 60 second sine-wave “chirp” rising from 50 to 1,000Hz over a period of 60sec
- This signal was fed into the resonant cavity from a loudspeaker embedded in the lower bout of the cavity top plate
- The microphone was held 80cm above the soundhole
- The signal coming from the soundhole was recorded using Audacitysoftware, then analyzed with the software’s Analyse / Plot spectrumfacility
- A series of drop-in soundholes allowed me to change the soundhole size
An important part of the method was to start each experimental run with a measurement taken with the soundhole completely blocked. This provided a baseline response and was subtracted from the response of each soundhole.
The downside of this is that it makes all measurements relative to the closed response. However, that is acceptable given that relative responses allow a clear analysis of the differences between soundholes. It also has the advantage of cancelling out the effects of speaker response, since the data used for each soundhole was its response above or below the closed box baseline.
Keep in mind that these results throw light on how the low frequency – bass – tones change as the radius of the soundhole increases. These are the frequencies are produced by the airbody inside the soundbox resonating.
Having got that out of the way, let’s look at some results.
RESULTS FOR ROUND SOUNDHOLES
Here is the signal spectrum for a series of soundholes covering the range from 35.7 to 54.9mm in radius. The graph shows the whole signal range from 50Hz to 1,000Hz.
Figure 4: Spectral response of round soundholes to chirp signal 
The radius of each hole is shown in the legend (R35.7 is a 35.7mm radius).
This shows that the cavity/soundhole combinations act in a very similar way to each other. No combination is capable of transmitting a complete version of the stimulating signal (50 to 1,000Hz sine wave), showing that each selects some frequencies to project while being unable to project others. This is the effect of the resonant frequencies of each cavity/hole combination.
The peaks in the graph are where each cavity/hole combination resonates in response to the signal. The resonant response is very similar for each combination.
By far the most sound energy projected is in the 100 – 260Hz range (notes G#2to C4 – fret 4 on string 6 to fret 8 on string 1, most of the range of a guitar). Given the evolution of guitar design, this is likely not a coincidence.
The area under each line is a measure of the power of the sound, so it’s clear that the largest soundhole (the green line R54.9) is the best emitter of the five holes.
The next graph zooms in on the 100 – 300Hz range.
Figure 5: View of main resonant peak for round soundhole response
The main difference between the five holes is that the larger ones transmit the signal more strongly than the smaller ones.
This is clearer in the next graph, which simply compares the largest hole with the smallest:
Figure 6: Response of radius 35.7mm and 54.9mm round soundholes to chirp signal
One difference is the larger hole’s activity between 500 and 550Hz, although this peak is not at all strong.
At first sight these results might be puzzling. Many acoustic guitar theory discussions maintain that smaller soundholes give a guitar better bass response, and larger ones better treble. This is not at all obvious from a glance at the data.
However, I will show that even though the spectral contour for all soundholes is the same, the proportionof energy radiated by smaller or larger holes does fit with the theory.
The next graph compares the total (relative)power radiated by each cavity/hole combination:
Figure 7: Relative power radiated from a range of round soundholes over range 50 to 1,000Hz
So it’s clear that the larger a soundhole is, the more effectively it radiates sound from the air cavity – the relationship of intensity to area is linear with a very good fit (R2= 0.9965).
There are some other differences as well that become clear if we look at how well the soundholes radiate at different frequencies.
Given that an acoustic guitar’s fretboard goes from E2(82.4Hz) to E5(659.3Hz) it makes sense to divide the 50 to 1,000Hz spectrum up this way:
|OCTAVE||FREQUENCY BAND (Hz)||GUITAR FRETBOARD RANGE|
|2||82 – 165||STRING 6 FRET 0 TO12|
|3||165 – 330||STRING 4 FRET 2 TO 14|
|4||330 – 660||STRING1 FRET 0 TO 12|
|5||660 – 1319||STRING 1 ABOVE FRET 12|
Here again is the set of responses from different radius round soundholes:
Figure 8: Response of round soundholes of different sizes
While the round soundhole responses show the same contour as each other, they actually radiate different proportionsof their total sound power in different octaves of the spectrum.
The next graph shows this clearly for the three spectral bands I chose (they are the bands based on the note E2at 82.4Hz – the frequency of the bass E string on the guitar – and two higher octaves covering the acoustic guitar fretboard):
Figure 9: Round soundhole radiation by octave for different radius soundholes
Notice how poorly all the soundholes radiate in the 660–1,000Hz band (the pale blue bar is hardly visible).
The next graph shows the same data but by percentage of the total for each frequency band:
Figure 10: Soundhole radiation by octave (% of total for each hole)
You can see that the bass response (in purple) of the 35.7mm hole is stronger than the others as a percentage of the total output– but of course its total output is lower than the rest.
If this behavior is the same in an actual guitar (which, remember, is not a rigid box like the one used to collect this data), soundholes become better at radiating in the 163 – 330Hz octave (Octave 3) the larger they get. Their low frequency response does in fact seem to tail off as a percentage of the total, as conventional wisdom suggests, even as their total radiating power improves.
So the bigger the soundhole, the more strongly it radiates, but there will be an upper size limit at which the structural integrity of the soundboard will be compromised and the vibrating soundboard surface area cut into. Making bigger soundholes would quickly begin to have an effect on the top’s vibrational modes as well, particularly the long dipole (see Appendix 8). 50mm is a good compromise.
More prosaically, a 50mm radius hole also makes it easier to get a hand in to make repairs than a smaller one. 
So generations of guitar makers have found a good size for round soundholes – but as is always the case there’s more to be said.
To sum up so far:
- Round guitar soundholes radiate most strongly in the band from 100 to 600Hz, and hardly at all in the higher frequencies
- All soundhole/cavity combinations select particular frequency bands that they are able to radiate strongly – the are unable to respond at any but there resonant frequencies
- The greater the area of a round soundhole, the more effective it is at radiating sound – the relationship between radiative power and area is linear (double the area gives double the projection)
- The greater the radius, the better the sound radiation becomes in Octave 3, central to the scale range of the guitar
- At this point we don’t know if these conclusions hold for a real guitar soundbox, which is not rigid – this needs to be checked (see Part 10)
CHIRP 12 in the graph title refers to the experimental run number using the chirp signal
Remember that all readings are relative to the blocked hole response
I used to employ my granddaughter with her small hands to help install pickups in my guitars because I was using 45mm radius soundholes at the time, thinking they would give better bass response.