PTSQ Series - 3: Dat sweet rumble tho

Or why timing is everything.

If you missed the previous posts, why not start with the first one :

PTSQ Series - 1: An ode to Engine Orders

If there is one aspect of noise that makes a (somewhat) consensus among the car enthusiasts community, it is that the “rumble noise” is a desirable feature.

Why exactly is that, though ? How is is generated and what are its controlling parameters ? Could any car, if modified, be made to rumble and what would it take ?

What am I talking about when I say rumble noise ?

The definitions may vary:

• Some might only refer to the pops and bangs, i.e. the unburnt fuel making its way past the engine cylinders and exploding/detonating in the exhaust line, which can be a result of a misfiring on idle or when revving the engine.

• Some might only refer to the very irregular tailpipe noise a lot of the older American V8 make (like the camaro Z28 below).

• Others (me included), will refer to any kind of noise that is beating, i.e. oscillating between loud and quiet more or less rapidly, unlike this Mini One’s exhaust noise for example, that emits a continuous low frequency tone, probably around 22Hz (as you would guess since this is a 4-cylinder engine idling around 700rpm, see the previous posts if that doesn’t make sense to you!) :

Here are a few examples or what I would define rumbly cars:

First of all is the classic, old school American muscle car irregular V8 burble:

Then there is a more regular V8 rumble, that europeans might be more familiar with (my go to relaxing soundtrack):

The fruuuuity burble of an E63 M6 V10:

The raucous burble of a Subaru Impreza WRX boxer 4:

And finally, the burble of this lovely Mercedes SL65 AMG V12:

In the NVH world, we often speak of amplitude modulation, heterodyning or beating to describe this phenomenon.

For a quick attempt at an explanation, this is how it goes:

Beating happens when two sounds waves, very close in both amplitude and frequency, interact with each other, generating constructive and destructive interference, resulting in a total sound wave whose amplitude will vary in time, being either twice as high as the sum of the sound waves or equal to zero.

Here is a more visual example:

On the vertical axis is the amplitude, on the horizontal axis is the time.

We have two different sound waves of equal amplitude but whose frequencies are very close to each other. One sound wave has a frequency of 40Hz (in orange) and an amplitude of 2 (we’ll deal with dBs later), the other sound wave has a frequency of 39Hz (in purple) and an amplitude of 2. When those two sound waves interact together, they merge to create a resulting sound wave (in white), whose frequency is 39.5Hz, its maximum amplitude being twice as high (4) and has an additional characteristic, a modulation frequency.

• A slow modulation frequency means that the amplitude of the third sound wave will vary slowly in time, i.e. you will hear the sound getting louder and quieter slowly, whereas a fast modulation frequency means that the amplitude will vary quickly in time, to a point where you might not be able to tell it is varying at all:

Slow modulation:

Fast modulation:

As usual, let’s start with the physical creation of the beating.

As we have seen before, the number of cylinders in an engine will determine what is its engine main order, i.e. the main frequency you will hear at any time an engine is running.

That was a lie.

Well, not entirely. A (slightly) more complete explanation is as follow.

For the moment being, we will focus on the tailpipe noise, as it lets us conveniently ignore the engine vibrations, i.e. the inertia forces generated by the movement of the crankshaft, the pistons and all the additional vibrations that can be caused by the (absence of) balancer shafts and counterweights. These will matter later, especially when we’ll talk about, in the final chapter of this series, the cabin powertrain sound quality design.

What matters for tailpipe noise then, more specifically for tailpipe rumble noise?

In order of importance-ish:

• Number of cylinders

• Cylinder firing order

• Exhaust headers relative length (i.e. the length when compared to each other)

• Exhaust headers geometry (i.e. the way the headers of one exhaust bank merge within each other)

• Exhaust bank mixing (more specifically after the catalytic converter or absence of :D)

• Exhaust pipes and mufflers design (more important for powertrain sound quality in general and regulations)

As this video from Engineering Explained summarizes (much better than I could), this all boils down to exhaust pulses timing in the exhaust:

Effectively, everything from cylinder firing order, to relative headers length and geometry basically impacts the spacing between these exhaust pulses, which translates to time interval between exhaust pulses, i.e., you guessed it, engine orders!

If that is unclear for you, remember that the time interval between exhaust pulses is equivalent to the frequency of the noise that you will hear, or go read my previous post about engine orders (yeah yeah I’ll stop reminding you, but still).

So, engine orders again, ok.

To better understand, let’s keep that Subaru boxer engine and let’s compare the unequal length headers to the equal length headers, using this video:

The first half of the video is with the unequal length headers (ULH), while the second half is with the equal length headers (ELH). Sure, both sound rumbly enough and we’ll explain why it is the case in a bit but the ULH definitely sounds like it has a more pronounced beating to it.

As is the case with these video dissections, let’s look at my favorite kind of drawings, the spectrograms, focused on the idling part of the two different configurations:

As usual, this being a 4-cylinder engine, we expect to find the 2nd engine order at the bottom and from there on we can deduce the higher orders. What do you think is the main difference between these two that contributes to the rumble ?

Well, if you were wondering why I explained the mechanism of modulation at the beginning, here it why it comes at play. When looking at the EHL spectrogram, we can see that the brightest (i.e. loudest) engine orders are integers and therefore quite distant from each other. Sure, there is a bunch of half-orders that light up as well. But when looking at the UHL spectrogram, we can see that the loudness is more equally shared between a lot more orders, integers as well as half-orders and this is what makes all the difference.

Effectively, as the video from"Engineering Explained” demonstrated, the unequal distance between the exhaust pulses will create more half-orders, which results in an energy distribution that will re-balance integer orders and half-orders. Which in turn means that all the sound waves interacting with each other have a frequency that is much closer one to another, compared to only having integer orders interacting with one another, but also that these sound waves are more likely to be of similar amplitude.

And what did we say favor amplitude modulation ? That’s right, similarity in both amplitude and modulation.

Here you go, that is the secret recipe that creates that sweet rumbling noise, dem half-orders and the energy they steal from the decent integer orders.

It doesn’t really matter which way you make it happen, whether its the headers design or the mixing between the two banks, if you want rumble, you’ll need half-orders. And that matters not only for idle noise, but for the whole of the powertrain sound quality in general, which we’ll explore in the next and (perhaps) final chapter of this series.

There is one more thing we need to address for the idle rumble noise, this time from a psycho-acoustic point of view.

Not all rumbles are created equal and not all rumbles are perceived equally neither. As a matter of a fact, most of the human population is the most sensitive to a specific modulation frequency, which is roughly around 4Hz. What does that mean ? Basically, if you have two noises of equal amplitude, that modulate at different frequencies, the one that modulates the closest to 4Hz will sound the loudest. While this has been measured on individuals during diverse experiments, there is no explanation as of yet to why this is the case but it would have something to do with pattern recognition, i.e. active filters rather than physical properties of our auditory system (link for the curious).

Thus, if the right engine orders interact with each other to produce a 4Hz modulation, this rumble will have more chances to be picked up by your brain and be perceived as such. Which means that at a given engine speed, there is only a limited number of engine order combinations that will produce the right frequency modulation.

These combinations will not be the same depending the engine speed, i.e. maybe that at idle orders 4th and 4.5th will create that rumble but at 4000rpm you will need to have orders 2nd and 2.5th to interact with each other.

In terms of amplitude, two factors matter:

• Firstly, your modulated sound wave’s amplitude needs to stand out from the background noise so that it can be perceived by the ear, so you need to make sure that the engine orders creating this modulation stand out themselves (the green scribble below) against background noise.

• Secondly, the modulation’s amplitude itself needs to satisfy a certain level. This simply means that if only the peaks of your modulated sound wave stand out against background noise, you’ll have a hard time perceiving it (the blue scribble below). You want as large a modulation as needed.

Visually, it would look like this (yay more poorly drawn stuff):

Effectively, if you have a modulating sound wave that is being drown out by non modulating sound waves, you won’t perceive it, hence my remark about the two examples of the EHL and UHL subaru being rumbly. They both have much louder exhaust noise than normal, more particularly louder high frequency noise, which favor higher half-orders, which in turn generate high amounts of modulation, which will be more easily picked up against the rest of the noise.

Finally, I haven’t addressed this topic yet but the human ear is not equally sensitive to all frequencies. For example, a 60dB 4000Hz noise will subjectively sound much louder than a 60dB 100Hz noise to the human ear. We’ll probably spend more time on this subject in a latter post but for the moment, this would mean that the higher the frequency of the noise you are trying to modulate, the high chance there is that this modulation will be picked up.

The limitation in the case of engine orders is two-fold:

• The higher you go in frequency, the bigger the separation between your orders is and the less likely it is that they will interact between each other. This establishes a ceiling on what order you can use for modulation.

• Usually, the higher engine orders are not as objectively loud as the lower ones and might get drown out .

All right, let’s summarize what is needed to have dat sweet rumble:

On the physical side:

• To have rumble, you need amplitude modulation of at least two sound waves.

• To have amplitude modulation, you need sound waves that are close enough in both amplitude and frequency.

• To have sound waves close enough in both amplitude and frequency, you need an equal loudness distribution between your half-orders and your integer orders.

• To have half-orders, you need to have unequal spaced exhaust pulses, whether it is through your cylinder firing order, your headers relative length or your exhaust mixing.

On the psycho-acoustic side:

• To perceive rumble, your frequency modulation should be as close as possible to 4Hz, meaning your choice of orders to make this happen is limited and will vary with engine speed.

• To perceive modulation, your resulting modulated sound wave’s amplitude needs to be higher than the background noise, preferentially by a margin.

• Your modulation’s amplitude itself needs to be large enough to perceived as such.

• The higher the frequency being modulated the better but there is a upper limit to the engine order you can use for this.

I hope you enjoyed this post, let me know in the comments !

If you missed the introduction to automotive NVH, check it out:

A story about cars, noises and vibrations