In the first part of this series, I discussed why I chose a Dodge (Mercedes-built) Sprinter 3500 SHC cargo van as the platform for a competition vehicle. This part delves deeper into the reasoning for this unorthodox vehicle choice. I'll determine the Sprinter's interior dimensions, and resulting resonance modes, both theoretically and experimentally. In addition, I'll experimentally determine the room gain, or "transfer function" across the frequency spectrum. Based on the experimental data, appropriate damping and barrier materials will be selected and installed.
Calculating Resonance Modes
Last time, I discussed the importance of favorable room dimensional ratios to evenly distribute room resonances. Axial resonance modes of a room may be calculated using the equation:
Where fm is the frequency of resonance mode m, m is the integer value of the resonance mode (1, 2, 3, ..., m), vs is the speed of sound in air, and d is the distance between the walls of interest.
In order to optimally distribute axial resonance modes in a room, extensive research has been conducted to determine the best dimensional ratios of a room. Table 1 shows, in order of descending quality, the best dimensional room ratios determined by M. M. Louden.2
The principle dimensions in meters and feet for the length, width, and height of the Sprinter interior were estimated from a CAD drawing to be 5.388m (17.68 feet), 1.684m (5.525 feet), and 1.855m (6.086 feet), respectively. The following room dimensional ratios were determined:
Height/width = 1.855/1.684 = 1.102
Length/width = 5.388/1.684 = 3.200
It should be noted that multiples of any dimension are also equally valuable. For instance, any value in the Y or Z columns could be doubled without detriment. From Table 1, it can be seen that the dimensional room ratios of the Sprinter rank 19th among the best dimensional room ratios, where the width corresponds to 1.0, the height corresponds to 1.1, and the length corresponds to 1.6, because the length at 3.2 is an exact multiple of 1.6. (See Table 1)
Given the speed of sound in air to be 344.42m/s (1,130ft/s), the axial resonance modes were calculated according to Equation 1. Table 2 shows the first 26 axial resonance modes for the length, width, and height. Figure 1 graphically represents the distribution of resonance modes. Although the distribution of resonance modes is reasonably uniform, both Table 2 and Figure 1 show three individual modes L3 (96Hz), W1 (102Hz), and H1 (93Hz) that are grouped more closely to one another than the rest of the modes. Continuing higher in frequency, two more modes, L6 (192Hz) and H2 (186Hz), are grouped more closely to one another as well. It would be reasonable to expect the van's frequency response to be altered by the presence of these more closely spaced modes and the lower fundamental modes at 32 and 64Hz. Although there are two coincident modes at 511Hz (L16 and W5), a seemingly undesirable situation, it's generally accepted by acousticians that modes above 300Hz are of little or no concern.3 The relevance of these theoretical predictions to actual measurements will be discussed later in this article.