PHYS341/2023/Project9
Reverberance Across the Guitar Top
Introduction
The guitar, like many other instruments, is one that is commonly associated with the sounds that strings create. Although strings are an important part of the sound of a string instrument, one commonality that is often overlooked that almost all string instruments have is the body. The body of a guitar allows for the vibrations of the strings to pass through the bridge and be amplified by both the material oscillating and reverberating itself, but also the cavity inside the guitar, and the sound hole from which the sound escapes. With this in mind, one difference between the body and strings is that the strings span across a large frequency range, whereas the guitar body has few modes of oscillation. The goal of this study is to understand the guitar body, specifically how the top of an acoustic guitar resonates in certain areas, and if certain areas amplify or resonate with higher amplitude at certain frequency ranges.
Method
In order to measure the frequencies of the areas, I will be tapping the guitar with my finger in four areas. I will use a dynamic microphone approximately one foot away to capture the different frequencies travelling through the air (since microphone diaphragms need movement of air to oscillate, I don't want to put my guitar too close to the mic).
For each area of the guitar top (A, B, C, and D), I will measure approximate ranges of peaks with the three largest amplitudes accompanying the fundamental (f1, fx, fy, and fz), which should provide insight as to which areas of the guitar resonate at certain frequencies. In other words, the fundamental, as well as the three loudest peaks behind it will be measured. I will determine which peaks are being amplified by analyzing the peaks in the spectrum graph.
To verify my data, I will recreate the experiment with certain areas being dampened with my hand to test if less reverberation of certain areas will reduce the frequencies once present in those areas and the other areas as well. My intention is to imitate a drum mute (moon gels). For the two areas with the lowest and highest (hertz) reverberation, I will mute said area and repeat the process. Each data point will be an average of 3 taps in one area to ensure the reliability of taps (this applies to the entire process).
Materials
- Acoustic Guitar (Taylor 114e)
- Dynamic Microphone (Sennheiser e835)
- XLR Cable
- Audio Interface (Focusrite Scarlett 2i2)
- Rag (to mute strings)
- Sound Proofing (chair + jackets)
Hypothesis
I predict that section A (top corner) will resonate with higher frequencies, as it is a smaller cavity in the guitar, and it also has a restricted area from which it can oscillate. Because of this, I believe that it will oscillate at higher frequencies than the rest. For section B (bridge), I predict it will resonate most with the middle-frequencies. The bridge is where the sound of the guitar transfers the most, and so, I am predicting that it will amplify frequencies with a fairly even distribution. It also has a larger area to oscillate in, but smaller area than the lower body, which is not reduced in size by the waist of the guitar body. Section C, (middle-lower body) I predict will be the most amplified at lower frequencies, as it contains the largest area for the guitar top to oscillate back and forth. I predict that section D may resonate with some higher frequencies, given that it is near the edge of the guitar body like A, but have more prominent mids as well due to its proximity to section C. I believe that the areas with the highest and lowest resonant frequencies will be sections A and C respectively.
Process
Part I
- Place the guitar upright, holding the neck with the audio jack/strap-pin on one knee to allow for maximal reverberation
- Record from ~1 foot away to allow the mic to pick up the sound through the air and not just the sound of the finger hitting the top
- Place a towel underneath and around the strings on the neck to prevent them from causing any additional interfering sound
- Tap section A three times with equal force and record the spectrum graph on audacity
- Record each fundamental, as well as the three loudest harmonics for each tap
- Calculate the average for each and record them in their respective data points
- To prevent error, repeat this step until all three taps amplify the same harmonics
- Repeat 1-3 with sections B, C, and D and record respective data points
Part II
- Place a hand on the area with the highest frequencies and repeat Part I
Part III
- Place a hand on the area with the lowest frequencies and repeat Part I
Data Analysis
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The results showed that the area with the highest and lowest averages were areas C and B respectively. Below will be an analysis of these sections organized by the three different parts of the experiment.
Part I: Control
The control test showed us multiple trends that I did not expect at first. Foremost, the fundamentals for each part were functionally the same (+/- 2Hz, could also be due to inconsistencies in taps). This may be due to the material that is being tapped, and so, the microphone picked up the fundamental and frequencies of the tap rather than the reverberance of the guitar afterward. That said, the reverberations can be heard in the audio files provided, although because microphones are more sensitive to higher frequencies (as well as our ears), the higher frequencies are more pronounced.
Note: I highly recommend using headphones (if possible without EQ, i.e studio headphones to more accurately listen to the present frequencies
B and C share a similar set of harmonics, as well as the same fundamental, and a similar shape of amplitude across the frequencies. Notable differences include the high end of these frequencies, where beyond approximately 1800 Hz, there is no sound detected. Area C on the other hand has frequencies ranging up to and beyond 5kHz.
Part II: Highs Dampened
With the highest average Hz are dampened (Area C) dampened, not much change occurred in the frequencies of the peaks that were present. Area B showed a steeper trend line after the highest peak. This implies that the amplitude of the lower frequencies was more prominent in the lower range than higher range. This is also displayed in the data table above. Area C showed no sound above 1400Hz (~4.6kHz difference). From this we can draw that it is possible that dampening for the most part only has an effect on the immediate area, and does not have a significant pitch altering effect on the fundamental frequency. It would be negligent not to acknowledge the lack of noise shown in the 0-30Hz range in comparison to the other graphs. I suggest that this may be due to the dampening of the largest area on the body, meaning the guitar would not reverberate at its natural frequency due to interactions with external oscillations in air in the room. The strength of the dampening may also have an alternate effect on the results.
Part III: Lows Dampened
The first noticeable comparison between the lows for both areas are that they contain the same (+/- ~5Hz) frequencies. In area B, the peak frequencies are in the same order, which is not expected, as that is the immediate area which is muted. I believe that this effect is present because the bridge itself does not necessarily oscillate significantly, but instead, it transfers the vibration into the guitar top which oscillates and resonates. So, muting the bridge (specifically right underneath the pins) and tapping it would not make a large difference in the immediate area. With this said, all three harmonics in Lows Dampened (L.D.) are at a much higher amplitude relative to the fundamental in the Control. Area C corresponded with the expected change, as the higher (Hz) peaks, specifically the second loudest peak in the Control became the loudest in the L.D. (174/180Hz).
Discussion
The results suggest that certain areas of the guitar top do enhance certain frequency ranges, but only insofar as the amplitude of certain peaks, and even so to a minimal degree. Dampening certain areas of the guitar gives reason to believe that different areas of the guitar amplify certain frequency ranges, as when those areas were dampened, the expected frequency ranges were quieter relative to the rest of the peaks. I was not correct in assuming that area A would amplify the highest frequencies, and that C would amplify the lowest. I was surprised that C would amplify the highest average frequencies.
There are many possible variables that may have affected this experiment, as well as some that could have yielded different results if pursued. The room acoustics may have played a role in the sound, however, that variable was mostly dampened by my homemade soundproofing setup. With that said, the natural external noises of my room most definitely could have had an effect on these results. Second, the tapping and the mic each have different possible variables that I would encourage the pursuit of. Distance to the mic would absolutely make a large difference due to the proximity effect (low frequencies amplified the closer one is to the microphone). The gain on the microphone would also change results drastically, and work hand in hand with the distance. This was tricky to perfect, as a low gain would reduce the attack of the tap, but not pick up crucial frequencies at low amplitudes. Inversely, a high gain would result in a peak when tapped, and possibly not accurately pick up the initial frequencies present, although it would be advantageous for sustained frequencies. One could possibly use a limiter in their digital audio workstation and increase the gain to resolve this problem.
This goes without saying; the hardness of the tap is also crucial. The material used to tap could also be altered, changing the timbre and possibly even the balance of frequencies. I do not think that they would change the frequencies themselves though, as the data suggests that the frequencies are dependent upon the material and thickness of the wood. Human error may have influenced amplitudes including inconsistent tapping, muting, and placement of guitar on the knee (muting from the bottom). I had also noticed when holding the neck, that squeezing the strings even when muted, changes the pitch of the taps. This brings into question the role that the strings play even when muted. I would like to find a means to confirm that the frequencies present are the frequencies of the guitar top reverberating, and not the frequencies of the tap itself. This could possibly be done with a high quality camera magnified and in slow motion, to count the number of oscillations per number of frames. Such could be compared to a sine wav generator placed in the soundhole of the guitar at different frequencies. Lastly, and most notably, I noticed that the peaks present did not seem to represent the familiar harmonic series. It would be expected that there be some other frequencies present, but there seemed to be a trend of frequencies coming in pairs. My prediction is that the back of the guitar would also resonate when the top was tapped. This may have resulted in altered frequencies for two reasons: first, the back of the guitar has no soundhole, and hence, a different shape. Secondly, the guitar back of the Taylor 114e is curved, changing the resonant frequency of the plane. I would guess that this slight difference would offset the back frequencies, resulting in the "paired" frequencies shown in the spectrum graphs.
Conclusion
With so many possible variables and uncertainties, I can only call this study inconclusive at best. With that said, there is reason to believe that the guitar top does resonate in and amplify certain frequency ranges relative to the area. I can say with reasonable certainty that the guitar top does have at least one resonant frequency, in this case, at approximately 92-98Hz. My hypothesis was incorrect, as areas B and C were the lowest and highest average Hz ranges respectively, not C and A. I think the most notable variables aforementioned in the Discussion section in no particular order were the inconsistencies, specifically in knee and hand placement, the microphone behaviour, the role of muted strings, ambient noise (not room reverb because of the soundproofing chair), and the guitar back noise. In a future experiment I would account for all of these carefully and with different tests to ensure that my data is accurate and correctly representing what I am attempting to study. It would be ideal to cross-experiment with things like a sine wave generator and high quality camera, in combination with a more diverse set of areas (namely the areas of different vibrational modes), although for the scope of this experiment, the results are sufficient to draw some conjecture.