Acoustic Resonance Characteristics of Birch Wood Loudspeaker Enclosures: Analysis of Influence of Shape and Filling

Abstract

This study presents a comparative analysis of a “design” speaker cabinet shape and a conventional block enclosure, both having identical internal volumes. Both enclosures were built from birch wood, and for comparison, block-shaped baffles were also made from medium-density fiberboard (MDF). While the designer’s new shape was handcrafted using a lathe, a cube baffle was made using a CNC machine. The block-shaped sound box was made as a representative of the classic shape that occurs most often in the world of music. For this reason, it is offered as an ideal reference sample of the enclosure for comparison with the new design proposal, which was produced based on the shape predispositions and the interest of potential customers. The loudspeaker systems were then subjected to anechoic chamber testing using the exponential sine sweep (ESS) technique to assess and compare their resonance characteristics. The box-shaped enclosure showed a smoother course of the frequency response, but the differences are not significant. A potential improvement in acoustic performance was offered by an acoustic dampening material that was incorporated into each enclosure, and the measurement was repeated. The drop shape from solid birch benefits most from filling, with an 8 dB reduction in low-end boom and 2 dB smoothing, resulting in more controlled bass. The cuboid of solid birch is quite stable even without filling, but filling still improves deep bass by ~3 dB and smooths mid-bass by ~2 dB. For comparison, the cuboid made of MDF shows the largest improvement with filling, with a 10 dB reduction in sub-bass peaks and 4 dB smoothing in dips. With the acoustic filling, the frequency curves are even more smoothed, and it can be said that the damping material can eliminate some of the imperfections of the enclosures.

1. Introduction

When researching speaker cabinets or enclosures, it is essential to consider the pre-dominant use of wood and wood-based materials in the industry. Agglomerated materials are often preferred for their uniform properties; however, the distinct properties of solid wood are significant and should not be underestimated [1,2]. Solid wood is characterized not only by its unique esthetics, but also by its natural composition, which is particularly valued in the current context [3].

In this research, we focused on the potential use and increase in the added value of preparatory wood species, especially birch. In the climatic conditions of the Czech Repub-lic, birch is an underappreciated preparation tree, but its properties and parameters make it certainly not an inferior tree. It is anticipated that with the projected decline of currently dominant commercial species, the prevalence of pioneer tree species in forest stands will rise. Consequently, the volume of wood from these species available on the market will also increase. Although often undervalued and considered to have lower economic worth, the potential of pioneer tree species for various applications has been extensively documented by several researchers [4,5,6,7]. For instance, Borůvka et al. [8] clearly demonstrated the feasibility of substituting beech wood with birch. Li et al. [9] highlighted the importance of leveraging this knowledge to promote the use of these species in products with higher added value. Among the pioneer species, birch has been the most extensively studied, though in certain regions, it is regarded not as a pioneer, but as a key commercial species. Studies on birch wood in Central Europe have been conducted by Borůvka et al. [8] and Dudík et al. [10]. In general, it will be necessary to pay attention to birch as such in Europe not only from the point of view of changes in climatic conditions, but also in a socio-economic context [11].

As observed in research [12], birch wood shows the highest values of acoustic wave resistance for both methods used to determine this parameter. In the ultrasonic method, birch wood had an average acoustic resistance value of 33.3 ×·10⁻⁵ kg/m²·s and in the resonance method, it was 32.6 × 10⁻⁵ kg/m²·s. In the case of maple wood, the mean acoustic resistance values were lower in both cases; they were measured at 25.9·× 10⁻⁵ kg/m²·s for the ultrasonic method and 24.9 × 10⁻⁵ kg/m²·s for the resonance method. Birch wood also achieved the highest mean values of the acoustic constant in both measurements, reaching 8.5 m⁴/kg·s in the ultrasonic method and 8.1 m⁴/kg·s in the resonance method. Požgaj et al. [13] reported slightly lower values for this wood species, at 7.5 m⁴/kg·s. For maple, values of 7.1 and 6.8 m⁴/kg·s were observed, which are higher than those reported by Požgaj et al. [13] and Bucur [14] in their work on maple wood, where a value of 5.8 m⁴/kg·s was cited.

The acoustic performance of loudspeakers is profoundly influenced by the design of their enclosures, including factors such as shape and material properties [15]. Although conventional shapes and commonly used materials dominate the market, they do not always yield optimal sound quality. This study investigates the impact of various design features on loudspeaker performance by measuring the sound pressure level (SPL), with a focus on how these factors can enhance or degrade acoustic output [16]. The sine sweep method is used to measure the acoustic properties of the loudspeakers, making it possible to evaluate how a given enclosure behaves across the frequency spectrum audible to the human ear.

While there are other techniques for measuring or simulating enclosure acoustics, such as the Finite Element Method (FEM) and Boundary Element Method (BEM) [17,18], this article is part of a broader study focused on the potential use of pioneer tree species. For this purpose, the chosen experimental method is sufficient to assess the suitability of the proposed enclosure shape. In this context, the unusual design and handcrafted production of the speakers play an important role, offering high added value to often underappreciated wood species such as birch [19].

2. Materials and Methods

Birch was chosen as a representative of the preparatory wood and therefore also the input wood for production. At the same time, thanks to its properties, it can be regarded as the ideal raw material for the production of speaker enclosures, as a product with added value. For comparison, we present the density values of silver birch (Betula pendula Roth) for the production of baffles, which was 630 ± 31 (AVE ± SD) kg/m³. The density values of MDF, a material often used for these purposes, are 749 ± 7 kg/m³. Additionally, as a representative of wood with good acoustic properties used, among other things, for the production of acoustic musical instruments, we present the density of sycamore maple (Acer pseudoplatanus L.), 602 ± 18 kg/m³, which was also used in the past for the production of identical baffles.

At the beginning, a design proposal was created, which was based on the already known resonance characteristics of basic geometric shapes. The spherical shape of the enclosure in Figure 1 shows the smoothest curve, and the block with beveled front edges with an eccentric speaker behaves well (Figure 2), but the spherical shape of the baffle is very complicated to manufacture. At the same time, the goal was to create a new design that would stand out among several loudspeaker enclosures due to its uniqueness. We decided on an interesting combination of already known shapes, and this resulted in a new sound box in the shape of a drop.

2.1. Production of Enclosures

The basis for this study was the creation of two types of baffles. The first is a hand-made baffle made according to the design proposal, as can be seen in Figure 3. This baffle was made using a lathe from naturally weathered birch wood. The second variant is a sound box in the classic cubic shape (Figure 4), which was made using CNC technology from the same birch wood trunk.

Both types of baffles were designed to have an internal volume of ~0.39 dm³, with a wall thickness of 10 mm and a weight of 160 g. The Autodesk AutoCAD 2023 drawing diagram showing the drop shape baffle section is shown in Figure 5. The enclosure was handcrafted using a lathe from a single piece of birch wood. Joiner’s lumber with a moisture content of 10–15% was used for its production. After the product was completed, the baffles were acclimatized to the parameters of 65% relative humidity and 20 °C.

The cuboid-shaped baffle was also made of birch wood using a CNC machine. It consists of four sides glued together on a miter and the back and front sides inserted into a half groove, as can be seen in Figure 6. All parts were glued together with PVaC wood glue Profibond D3 (Profil Print Technology s.r.o., Písek, Czech Republic). The walls of the baffle had a wall thickness of 10 mm as well. After production, the enclosures were also climatized to the parameters of 65% relative humidity and 20 °C.

The same wood species offers an ideal opportunity to compare the designed drop-shape sound box with the well-known block shape. Each shape of the enclosure was produced in triplicate, and the frequency characteristics were measured on all six enclosures in order to eliminate manufacturing errors as much as possible, which could show up during the measurement.

The damping material used inside the loudspeaker enclosure was glass wool with a nominal density of 45 kg/m³. Given the very small internal volume of the cabinet (0.39 L), a complete fill would correspond to approximately 17.6 g of the material. In practice, only a fraction of this volume was employed; the enclosure was filled to about 10% of its volume, corresponding to a mass of roughly 2 g. The glass wool was applied in a loose, non-compressed layer, distributed evenly along the interior walls of the cabinet. This configuration ensures sufficient absorption of internal standing waves while preserving the effective acoustic volume of the enclosure and avoiding excessive damping.

The speaker driver that was used to measure the characteristics of the individual enclosures was the same each time to make the results comparable. Specifically, it was a Dayton RS 75-4 converter (Dayton Audio, Springboro, United States of America). The converter characteristics are listed in

Table 1. Speaker driver characteristics.

Impedance	4 Ω	Sd	12 cm2
Re	3.1 Ω	Vd	1.31 cm3
Le	0.72 mH @ 1 kHz	BL	2.01 Tm
Fs	177 Hz	Vas	0.14 l
Qms	5.76	Xmax	1.1 mm
Qes	0.97	VC Diameter	16 mm
Qts	0.83	SPL	85.2 dB
Mms	1.1 g	RMS Power Handling	15 W
Cms	0.72 mm/N	Usable Frequency Range (Hz)	170–20 000 Hz

below.

2.2. Software and Measurements

Utilizing the Room EQ Wizard—REW V5.20.13 (John Mulcahy, Sheffield, UK) software for room acoustics and audio analysis, we measured the Sound Pressure Level (SPL). This is a crucial metric in audio engineering, as it quantifies how loud a sound is perceived as and is essential for evaluating the performance of audio equipment, including loudspeakers. The sound pressure level is defined as

$$SPL\left(dB\right)=20log\left({\displaystyle \frac{p}{p_{ref}}}\right)$$

(1)

where p is the acoustic pressure and p_ref is a reference pressure. The factor of 20 comes from the fact that the intensity of the sound wave is proportional to p². For sound in air, the reference pressure is defined as 20 μPa (2 × 10⁻⁵ Pa).

Measuring the Sound Pressure Level is essential for understanding and optimizing loudspeaker performance. The REW software makes it possible to easily conduct precise SPL measurements, analyze frequency responses, and make informed decisions to enhance audio quality in various environments. Whether for home audio setups or professional sound systems, SPL measurements provide valuable insights into loudspeaker behavior and acoustic performance [20].

Figure 7 shows the user interface of the REW software. This software is used to measure the sound pressure level (SPL), which we deal with in this article. REW can also be used for other measurements, such as Frequency Response measurements, which reveal how different frequencies are reproduced by the loudspeaker or audio system. Impulse Response captures how a system reacts to a short burst of sound. Waterfall Plot Analysis visualizes the decay of sound over time for different frequencies. Phase Response Measurement analyzes the phase relationship between different frequencies. Room Mode Calculations identifies problematic low-frequency resonances in a room. Cumulative Spectral Decay Plot displays energy decay over time for different frequencies. Equalization Suggestions generates recommendations for EQ adjustments based on the measured frequency response. Speaker and Microphone Calibration allows for the calibration of measurement microphones to ensure accurate readings and provides a means to correct microphone sensitivity and frequency response. Multi-Channel Measurements supports measurements for surround sound systems and multi-channel setups. Comparison of Measurements enables users to overlay various measurement graphs to compare performance under various conditions (e.g., different speaker placements or settings).

In this study, we employed the exponential sine sweep (ESS) method, commonly referred to as “retuned sine” or “sine sweep” [21]. This technique was implemented to accurately measure the loudspeaker’s impulse response. The methodology involves exciting the system with a harmonic signal whose frequency increases over time in an exponential manner. The system’s response to this signal is recorded, enabling the extraction of the impulse response through subsequent processing. This can be achieved either by filtering the recorded signal with an inverse filter or by performing division in the spectral domain, though the latter method does have certain limitations [22].

One of the significant advantages of using the ESS method is its ability to separate harmonic distortions from the primary response, thereby providing a clearer and more accurate measurement of the loudspeaker’s performance.

The obtained impulse response characterizes the entire system, therefore it is necessary to specify the complete measurement setup and any other factors that can then be more or less eliminated. The measurement configuration employed in this study was as follows.

Recording:

• Notebook running REW V5.20.13;
• RME Fireface UC sound card;
• Microphone cable (balanced line);
• Earthworks M23 measurement microphone.

Reproduction:

• Notebook running REW V5.20.13;
• RME Fireface UC sound card;
• Unbalanced cable;
• GHXAMP TPA3116 amplifier (considered for future use with loudspeakers);
• Speaker cable;
• Tested loudspeaker.

For this study, the measurements were conducted at a high sampling frequency of 192 kHz with a 16-bit depth, ensuring detailed capture of the audio signal. The duration of the sine sweep was set to 512,000 samples, equivalent to 2.7 s [23]. This duration was deliberately chosen to be longer than the room’s reverberation time to avoid any adverse effects on the measurement accuracy. To ensure reliability, each measurement was repeated four times and each wooden enclosure was climatized to 65% relative humidity and 20 °C.

The timing reference for the measurements was maintained using the feedback connection of the sound card, ensuring precise synchronization. The loudspeaker system was strategically positioned at a height of approximately 1.5 m. The microphone, essential for capturing the audio response, was placed at a distance of 0.5 m from the loudspeaker. This setup was designed to optimize the accuracy and reliability of the measurements, thereby facilitating a comprehensive analysis of the loudspeaker’s impulse response.

3. Results and Discussion

The output of the measurement of the acoustic parameters are graphs showing the frequency and impedance characteristics of the loudspeaker inserted in different types of enclosures. The areas of all the graphs are determined by the frequency range of 20–20,000 Hz. The sound pressure level is in the range of 30–100 dB. For greater clarity, the curves are smoothed by a value of 1/12.

Given the absence of significant sound differences between various types of wood in prior research [12,24], our study primarily focuses on comparing different baffle shapes and the impact of acoustic filling, as illustrated in Figure 8 and Figure 9. First, we evaluated the differences between the teardrop-shaped baffles made of birch wood, comparing those without damping material to those with damping material [25].

The results for the birch shell in Figure 8 show the change in the course of the frequency curve in certain areas. As with the other figures, this plot represents the average response curve derived from measurements on three enclosures. The most noticeable deviations are in the sub-bass region (20–60 Hz). Below ~30 Hz, the red line (with filling), i.e., response, is significantly lower (~5–10 dB less) compared to no filling. The blue line (without filling) shows higher SPL in this range, with a broader and more pronounced hump between 20 and 30 Hz. This suggests that acoustic filling dampens the resonance in the lowest frequencies, especially below the system’s tuning frequency. In the area around 40–60 Hz, the red line shows a more controlled and smoother rise. The blue line has a notable dip around 45 Hz, possibly due to internal standing waves or resonances that are tamed by the filling. Around 60 Hz, both lines converge. There are also deviations around 1500 Hz in the midrange, where the effect of the damping material is noticeable, which makes the frequency response smoother [26,27]. The deviations are probably caused by standing waves in the space. Thanks to the damping wool, this resonance is reduced by about 2 dB. There are no significant differences in the curve except for the larger deflection of the undamped enclosure.

The frequency curve shown at the bottom shows the ripple caused by the resonance of the enclosure in addition to the main deflection caused by the speaker. It is located at the same frequency as the frequency response. It is largely eliminated by the damping material and is therefore particularly noticeable in the curve showing the undamped case. Differences in the main deflection of the compared prototypes may be due to measurement errors.

Figure 9 shows the frequency characteristics of the birch box enclosure. The main differences can be seen below ~35 Hz. In this area, the enclosure with filling (blue line) has slightly lower SPL (~3–5 dB drop) compared to the unfilled box. This is a small loss in deep extension, consistent with added internal damping. Around 35–50 Hz, the green line (box without filling) shows more pronounced irregularities, including a dip at ~45 Hz and a small peak around 38 Hz. The blue line (with filling) smooths these irregularities slightly, suggesting reduced standing waves or internal reflections. Around 60 Hz, both lines converge and show minimal difference.

The frequency characteristic curve also undulates in the frequency range around 1700 Hz in mid frequency, where the influence of the speaker becomes apparent. In this case, it is also a resonance of the return wave in the enclosure. The unwanted vibration of the enclosure is also caused by the diffraction effect, which occurs on the front edge inside the box-shaped enclosure. After damping material has been added, the deflections are suppressed and reduced by 2 to 4 dB.

Furthermore, there is a slight protrusion of the undamped cabinet curve around the 1700 Hz region, for the same reason as the frequency deviation in the same part of the graph. Even here, the peak could be eliminated by using damping material.

When comparing both shapes, it can be said that the cuboid enclosure is less affected by acoustic filling than the drop-shaped enclosure in terms of SPL response. In the drop-shaped box, the filling caused a more significant reduction (5–10 dB) in the sound pressure level below 30 Hz, whereas in the cuboid enclosure, the change was smaller (3–5 dB). This suggests that the drop shape may generate stronger low-frequency resonances, which the filling damps more effectively.

In the cuboid enclosure, the effect of the filling is mild but still beneficial. While the improvements are less dramatic than in the drop-shaped design, they are still worthwhile for improving accuracy and reducing unwanted resonances. The filling is particularly beneficial for the drop shape, which likely produces internal resonances due to its non-parallel walls and complex internal geometry. Acoustic filling helps suppress these resonances, resulting in a more controlled and accurate low-frequency response—albeit at the cost of some deep bass extension.

Figure 10 shows the frequency characteristics of a block cabinet made of medium-density fiberboard. The MDF baffle was made for to enable the comparison with a representative of this frequently used baffle material [28]. The MDF box shows major low-frequency resonance without damping. Acoustic filling greatly improves smoothness by absorbing excess energy at the cost of SPL under 30 Hz. A comparison between Figure 9 and Figure 10 shows that the differences between the individual curves are very negligible. This enables the use of preparatory woods and increasing their added value. In addition, the acoustic properties (especially of birch and poplar) are comparable to, for example, maple, which is used to make musical instruments [12,24].

To summarize the findings from all the measured enclosures and configurations,

Table 2. Overall quantitative conclusions about the effect of the filling.

Category	Solid Birch		MDF Cuboid-Shape
	Drop-Shape	Cuboid-Shape
Sub-bass resonance (<30 Hz)	−8 dB	−3 dB	−10 dB
Dip smoothing (40−50 Hz)	+2 dB	+2 dB	+4 dB
Effectiveness of filling	High	Moderate	Very high
Need for filling	Strongly recommended	Helpful but optional	Essential

presents a comparison of the acoustic effects of the different shapes and materials, and the use of acoustic filling. The focus is on sub-bass performance and the extent to which filling alters the SPL response. This provides a clear overview of how each design behaves and of the practical benefits of internal damping.

Each of the enclosures has its pros and cons. In the case of the teardrop-shaped enclosure, standing waves occur inside the space and the frequency characteristics are thus adversely affected [29]. On the other hand, with a box structure, there is, as can be expected, a diffraction effect caused by the sharp edges inside the enclosure [30,31]. We tried to eliminate this phenomenon, and that is why we created a drop-shaped design, in which there are no sharp edges [32]. However, it can be seen from the graphs that despite the diffraction effect of the box-shaped enclosure, it has a smoother frequency response than the drop-shaped enclosure. However, the differences are not significant [3,33]. By using the inner filling, these differences were even more mitigated. It can therefore be said that the damping material has a positive effect on the frequency response if the enclosure shows any imperfections, which is also reported in publications by Newell and Holland [3], Eargle [34], Walker [35] and Bauer [36]. However, it must be added that this solution is not entirely ideal, and that it would be better to focus further research on the development of a new, better design of the enclosure, which would offer not only an innovative appearance, but also an ideal course of the frequency curve, even without the need to install internal filling. For further research, for example, a box design with rounded inner edges and a sufficiently rigid structure to prevent unwanted vibrations of the enclosure walls may appear to be ideal [37,38]. It would also be advisable to use a bass-reflex on the back of the speaker [39,40].

4. Conclusions

When evaluating the frequency characteristics of the loudspeakers, clear differences were observed between the cube-shaped and the teardrop-shaped enclosures. Specifically, the cube-shaped housing demonstrated a more consistent and balanced frequency response compared to the teardrop design. These results highlight the critical impact of cabinet geometry, both external and internal, on sound propagation. In the case of the drop-shaped enclosure, it was necessary to address standing waves and the more complex internal geometry. This was successfully mitigated by the use of internal acoustic filling. As a result, the frequency response curve became smoother, and the loudspeaker delivered a more consistent output with an 8 dB reduction in low-end boom and 2 dB smoothing, resulting in more controlled bass. Additionally, the design offers added value through the originality of the hand-made enclosure shape and the use of an underutilized pioneer wood species. However, it is important to note that, while these differences are measurable, the extent of their impact may vary, depending on specific design parameters and environmental conditions.

In the further development of wooden loudspeaker enclosures with unconventional shapes, the focus shifts more toward acoustic performance than handcrafted production. To support this, the design process increasingly relies on advanced methods, such as simulating internal acoustics using COMSOL software prior to fabrication. This approach will help explore the boundaries of audio engineering and enclosure design, extending beyond the use of pioneer wood species.