Before getting started we need to refresh some basic knowledge to understand how the sound is generated.
Sound is a pressure variation in the transporting medium (usually air) which produces an auditory sensation in the receiver. We can differentiate non-periodic sounds, which are considered noise, and periodic sounds (each of these with an specific tone, pitch and intensity). The frequencies that humans can perceive range from 16 Hz to 20,000 Hz.
As noted above, the sound is defined by three characteristics:
- Intensity is the feature that defines the energy carried by the sound wave. In the graphic representation, it will be the amplitude of the wave.
- Frequency is determined by the number of oscillations of the emitting object per unit of time. Our brain feels the sounds with lower frequencies as deeper and higher frequencies as higher pitched.
- Tone is the third element that defines a sound. Graphically it corresponds to the shape of the sound wave. Every sound is composed by several harmonics, these allow us to differentiate between the same note coming from a piano or a violin. The differences in intensity between harmonics define the tone of each sound source. Harmonics are integer multiples of the fundamental frequency. A sound whose fundamental is 60 Hz has its first harmonic at 120 Hz, the second at 240 Hz, and so on.
Although there is some discrepancy in the methods used for the calculation of the fundamental frequency in a 4-stroke engine, I like the position which states that the fundamental frequency is generated by the crankshaft revolutions, while the dominant harmonic is produced by the explosions in the cylinders . According to this, we can calculate the fundamental frequency by converting the engine rpm into frequency in Hz:
60rpm = 1 rev/s = 1Hz \\ Fundamental frequency (Hz) = rpm/60
As stated above, the dominant harmonic is produced by the fuel explosions in the cylinders. A four-stroke engine reaches combustion phase every two turns of the crankshaft. In the case of a 4-cylinder engine, two explosions will take place at each turn, 3 explosions in a 6-cylinder engine, 4 in an 8 cylinder engine, and so on. Therefore, the dominant harmonic will be a multiple of the fundamental frequency:
Dominant harmonic (Hz) = Fundamental frequency * (number of cylinders / 2)
Using these calculations for a V8 engine turning at 2000rpm:
Fundamental note: 2000rpm/60 = 33.3Hz (C1)
Dominant harmonic: 33.3HZ * (8 cylinders / 2) = 133.3Hz (C3)
Internal combustion engines and their exhaust systems are very similar to musical instruments, as they have different musical and harmonic notes, explained by the physics of the exhaust gas pulses and the course that the gas follows through the exhaust system.
The higher engine revs, the more frequently the gas pulses travel through the exhaust, increasing therefore the pitch Similarly, as these gases also travel at a higher speed with higher revs, the volume (intensity) will also increase.
The engine sound comprises several harmonics based on the size and number of cylinders, their arrangement (V-engine, in-line, boxer…), ignition order, and so on. These harmonic frequencies can be tuned by modifying the length and diameter of the exhaust pipes, installing resonance chambers and even using different materials for each part of the exhaust.
Ignition timing is of great relevance. In an engine with a uniform ignition timing each cylinder will reach the explosion after exactly the same time as the previous cylinder. Thus, in a 4-cylinder engine an explosion will take place every 180º, in a 6-cylinder engine every 120º and in an 8-cylinder engine every 90º.
In any case, not all engines have an uniform ignition timing, for example Opels C25XE, a V6 engine with a 54º angle between cylinder banks. Due to the arrangement of the cylinders, some explosions happen closer to each other than others, causing an irregular flow of exhaust pulses.
The following graph shows the pressure differences in V8 engines with flatplane crankshaft (red) and crossplane crankshaft (blue). The first graph represents the right cylinder bank and the second represents the left cylinder bank.
Not only the ignition timing is relevant, but also ignition order (the sequence in which the cylinders reach explosion phase). Let’s take as an example a V8 crossplane engine, where two consecutive exhaust pulses are generated in the same bank, generating irregular exhaust flow which results in a guttural sound, trademark of crossplane V8s.
The same is valid for those exhaust systems in which the lengths of the primary pipes are not equal, making the exhaust pulses reach the manifold irregularly.
The exhaust system will generate a high intensity harmonic that will vary depending on the length of the primary pipes, the longer they are, the deeper the sound will be, just as it happens in a wind musical instrument. Think of a trombone, where you can change the sound pitch by lengthening the path followed by the air. Likewise, the diameter will have a direct influence on the sound; the larger the diameter, the lower the exhaust gas speed and therefore the lower the pitch will be.
By modifying the lengths of the primary pipes and how they reach the collector you can get very different sounds. We cannot change the order of ignition of an engine, but we can alter the order and the moment in which the exhaust pulses reach the collector. One of the best examples of this are the 180º collectors in V8 crossplane engines, where main pipes cross from one cylinder bank to the other to reach the opposite collector, so that the exhaust pulses arrive uniformly to both collectors.
There are still elements that allow the sound tune after the collector, the most important of them all being the resonator, which is used to eliminate unwanted noise frequencies.
The dimensions of the resonator are designed in such a way that the waves reflected in the resonance chamber help to cancel certain unwanted frequencies of the exhaust sound.
When a wave enters one of the holes in the resonance chamber, it travels through it until it is reflected in the chambers walls. The size of the resonance chamber is calculated in a way that the reflected wave reaches the output just when the next wave is being reflected on the walls of it. Thus, the high pressure zone of the first wave will be aligned with the low pressure zone of the second wave, canceling both in the process.
Since the reflected wave will have lost energy in the process, the cancellation will not be total, as we can see in the graph.
In engines divided in two banks there is one more element that can affect the quality of the exhaust gas flow and therefore the sound. It is the connecting element between the tubes behind the collectors of both banks.
In an engine with irregular ignition timing, where two cylinders of the same bank have consecutive explosions, nothing is happening in the opposite bank and the exhaust pipes are empty. Therefore, interconnecting the tubes of both sides allows the pulses to scavenge the remaining gases on the other side.
In an H-pipe, the exhaust gases are scavenged to the other side because of the Venturi effect, which is reduced as the rpm rise. The solution to this problem is an X-pipe. In this case both sides merge into one to split again, allowing the exhaust gases of each bank to flow freely through both tubes and leveling up the pressure differences.
A crosspipe affects the exhaust sound by increasing the pitch because the exhaust flow gains speed through this section.
I hope that this has been of your interest. Thank you for reading me!