Sound Reproduction and the Limitations of Hearing

The sound reproduction assignment was part of a module I shared with the Audio and Music Production course. Was rather challenging for someone who hadn’t thought about audio much before!

This was one of the first “long” pieces (can’t really call it long now after a 140-page dissertation) based around audio. An honestly overlooked aspect of videos more often than not. Although this wasn’t one of my finest pieces (72%) I’m still posting it as a means of showing general understanding of the concepts.

That all being said, it’s full title was pretty epic for what is a technical document, “Investigation into the physical laws that govern Sound Reproduction and the limitations of human hearing”.


Reproducing Sound and Human Hearing

In order to reproduce sound, you first need to understand that sound is caused by variations in sound pressure. In essence, if we are going to reproduce a sound we need to be able to measure and then reproduce that pressure. It is this sound pressure wave which then interacts with our ears and is interpreted by our brain as sound.

We measure waves firstly by their frequency, which The Physics Classroom (2010) defines as, “the number of complete back-and-forth vibrations of a particle of the medium per unit of time.” By this, we mean in sound it is the number of times a full cycle of the sound wave occurs within a second and we give this value in Hertz (Hz). The second key aspect of measuring sound is the wavelength, which in a repeating sound is called a period and this is the minimum time interval where this sound can repeat. For a high frequency wave, this period is shorter than that of a low frequency wave. Because of this, we can use a simple rule whereby if you double the frequency, you halve the period.

(High and Low Frequency Waves, 2010)

Reproducing sound at is core is all about re-creating the sound pressure wave as accurately as possible. There are many things that can create this, from the human voice, to musical instruments and loudspeakers. What is of equal importance is how the human ear interprets these sound waves along with the brain.

Firstly, the sound wave enters the ear and makes the ear drum vibrate. This in turn makes the small bones inside the ear move, resulting in the fluid that contains the cochlea to move. It is this precise movement of fluid which is then picked up by the auditory nerve and interpreted by the brain as sound.

A labelled diagram showing a cutaway of the different parts of the human ear, from the outer ear through the middle ear to the inner ear.

(The Human Ear, 2016)

Thanks to this design, the human ear has a large range of pressures that it can hear. This starts at the threshold of hearing, which is 0.00002 Pa, which has been set on the SPL scale as 0dB. Sound becomes painful to hear due to the effective power behind the pressure (sound intensity) which can cause damage to the ear. This level is around 130dB or 63.2 Pa.

Image result for loudness equivalent pascals

(Table of Sound Levels, 2005)

We use the decibel as the main measurement as it is a more simplistic scale for calculation and is far easier to use when comparing different sounds to each other. However, the Sound Intensity shown in the table above goes to show just how large the range of human hearing can be.

What is High Fidelity?

“I invented the phrase ‘high fidelity’ in 1927 to denote a type of sound reproduction that might be taken rather seriously by a music lover. In those days the average radio or phonograph equipment sounded pretty horrible but, as I was really interested in music, it occurred to me that something might be done about it.” – Hartley, H. A. (1958).

In the simplest terms, the above quote still applies to this day. For sound reproduction, it is used when a speaker can accurately reproduce sound across a range of frequencies, without distortion generally or with uneven reproduction across octaves. For a lot of cheaper speakers, they are very rarely producing the pure tone. Often, they produce harmonies of the tone, as well as create other issues related to this in the environment around them.

Getting the loudspeaker to accurately reproduce this in the first place just by design is paramount, whereas if the decision is made to opt for a cheaper speaker, you can attempt to compensate for inaccuracies with a graphic equaliser for example. However, consideration must be given to the environment as even the best speakers can be undone with issues like standing waves and reverberation, both of which can distort the sound.

The examples above are some of the core aspects in picking the right speaker and companion equipment for the right task, as will be shown in the examples below of certain loudspeakers for different situations.

Loudspeakers for Sound Reproduction

To get completely accurate sound reproduction is almost an impossible task. Many manufacturers would like to say that their loudspeakers have the best sound reproduction, however this is often something that is not even in the manufacturers hands.

Firstly, is the quality of the recording being delivered through the speakers. You can have an excellent speaker, yet if the recording is of a poor quality, then the reproduction will suffer. This is what a lot of early recordings suffered from, as they had no accurate way to record the original sound so when the speaker came to reproduce it, you only ended up with a poor result.

The second aspect is the environment the loudspeakers are being used in. Again, you can have what in a certain environment could be a good speaker (as you will see with some of the examples below).

Although many examples could have been given here to loudspeakers which are technically accurate, as there’s no way of knowing where and what you are playing through them, the answer here is the best speaker is simply one which you enjoy listening to.

However, if it is accuracy that is needed (rather than “nice” sounding), then the design of choice is usually a high-quality studio monitor speaker. Taking the example of the Tannoy Reveal 802, when compared to some of the speakers below, these have a surprisingly large frequency response of 42Hz – 43kHz (Tannoy, n.d). It achieves this through what is essentially a ported enclosure that is tuned to support the base end frequencies, so even though the unit only has an 8” woofer and 1” tweeter, many studios use them as a reference point for listening back to sound accurately. Other examples will be shown in the section below for home and studio design, yet this carefully designed enclosure does show that size isn’t everything when it comes to accurate sound reproduction.

(Tannoy Reveal 802 Frequency Response, 2014)

As you can see, which the quoted frequency response range from the manufacturer, the tested result shows that even this is not perfect, especially from the 42Hz bottom end. However, the base end does then benefit from have the ported enclosure, as shown by the bloom at ~150Hz. However, the rest of the frequency response shows a relatively balanced output, which goes some way to explaining the good reputation this model has as a well-priced (£205) monitor. However, this also shows as an example of how difficult the task is to get a flat response.

Loudspeakers for Public Address Systems

The first differences you will see with PA systems is if the speaker is active or passive. Deciding on this can have an impact on your setup. For example, active speakers have built-in power amplifiers and crossovers, making them excellent for portability as it means you won’t need to bring an additional external amplifier for example. This makes them ideal for touring bands who have limited space for equipment or just a more simplistic setup. However, for most large-scale PA systems, you’re ideally going to want full control over every aspect of the setup, which means going with passive speakers. (Sweetwater Sound, 2013).

2-way speakers (driver and tweeter) are the most common starting point for a setup, yet you can just as commonly have 3-way designs for PA systems (driver, tweeter and woofer). However, within this you tend to get a certain type of enclosure design too. One of the most common (seen on the expensive example below) is the ported (or bass reflex enclosure). This is where the internal air pressure is pushed out of a port in the enclosure, with the aim to boost the overall sound level. The main downside over a completely closed enclosure is there is not as much air pressure to support the driver itself, which can make the sound production less precise.

QW4 Frequency Response from official Manual (n.d)


Yet when you have brands like Peavey charging $2499 for a 3-way QW4 which contains essentially a tweeter and two 15” speakers (Sweetwater Sound Store, n.d) it is hard to understand what you are getting for your money. In truth, the manufacturers tend to focus on a few things, namely power handling, efficiency and frequency response. Continuing to use the Peavey QW 4F as an example, the cost comes from things like the cones of the 15” speakers are built with Kevlar, which has the advantage of them being strong, yet light; making them efficient. Within that, you then have a 50 Hz – 18 kHz frequency response, all while having a 2800 watts program, 5600 watts peak for power handling. It is this sort of speaker which would be ideal for a very large open venue, yet because of the cost of a single speaker, this opens up options into having multiple speaker setups (or stacks) to obtain the same or better result for the cost. For example, the Behringer VS1520 has a 15” woofer and a tweeter, yet it is $225. This will be down to the materials used in the build, as well as its power delivery (600W peak), however within that it has a similar frequency response of 50Hz-20kHz.

The problem here comes with the setup of these speakers. You might get 10 of the Behringer speakers in a stack or array to give you a far more flexible setup than the cost of a single Peavey QW 4F, yet within that comes the complex task of balancing the sound out of all 10 speakers, not to mention the potential amount of rigging needed.

As you go into other venue types like churches, concert or other types of hall spaces, you still end up with the same concepts as with larger venues, just on a smaller scale. Put simply, you don’t need as much power to fill the space, plus now that you start adding in walls again, you must take more consideration to impacts on reverberation and mitigating standing waves. Here, as the sheer size of the speaker is not so much of an issue, manufacturers can focus a little more on the accuracy of the sound. One such example is the Yamaha BR10 (Yamaha, 2012) which although its main speaker is only 10”, it still has a similar frequency response of 65Hz-20kHz. This is only really as it is slightly too small to produce the base sounds, yet the tweeter is still a similar size. Going back into the enclosure design, as the sheer volume of sound is not so crucial, there is less benefit for ported enclosure designs, so the majority are sealed enclosures.

Finally, a popular design for outdoor spaces have been horn speakers in the past. This is mainly as horn designs (if made cheaply) often have poor sound accuracy as they can distort the sound. Yet for an open-air concert where the precision of the sound is not so key, this loss of quality can be acceptable for the benefit of greater volume.

Loudspeakers for the Home and Studio

With home loudspeakers comes a new consideration; style. There are also new use cases, like PC speakers to consider. Starting with PC speakers, these tend to be quite small as they are normally designed to sit alongside a PC monitor and be unobtrusive in their size, while still providing a reasonably good quality sound. Many manufacturers get away with this by having the sweet spot for the speakers be roughly where someone would be sitting at a desk, meaning that the sound is acceptable for that specific setup, yet take them away for a larger setting and they are poor. Thus having a sound reproduction of sufficient quality for purpose.

Here, you will still see ported enclosures to provide a larger frequency response, even though the main speaker (and driver) used are often small. However, through smart design, you can still get an excellent frequency response.

(Edifier Spinnaker Measurements, 2016)

Outside of a slightly boosted base end, the results for this loudspeaker goes to show that with both smart design, as well as digital signal processing, it is possible to obtain good accurate sound. From the image below, this is down to a very compact 3-way design comprising of a small tweeter, mid-range and woofer.

(Edifier Spinnaker, 2016)

From this design, you can see that (although small) each part of the system has a specific frequency range to work with and thanks to the careful design of the enclosure and the choice of speakers and drivers, an accurate (yet not particularly powerful) loudspeaker has been created.

Up until this point, these examples have shown that the fundamental physics and maths behind sound reproduction are the same, regardless of the size of the loudspeaker being made. However, with style being a factor, some manufacturers have resorted to unique approaches when it comes to design.

With sound being created essentially by the vibration of air creating the pressure wave, the electrostatic speaker has become popular for home use for those looking for slim and unique looking loudspeakers in their home.

Based on the varying electrical audio signal, the diaphragm is alternately charged with a positive current and a negative current.

Electrostatic Speaker (2001)

It is the positive and negative plates that create the electromagnetic field to vibrate the diaphragm to create your sound.

For the example of the Sanders Sound Systems Model 11, however, the overall response is more inconsistent if you compare it to that of a traditional driver. Fundamentally, you are vibrating a large piece of metal, so once you start this moving, even with the best magnets and design of conductive plates in the world, it’s going to be very difficult to get the whole diaphragm vibrating at different frequencies consistently.

Model 11 SPL Plot (2013)

All told, speaker design here still abides by the fundamentals of maths and physics. The more you focus on quality of the drivers and case design, the better the product you can produce. However, that also drives up cost which in some cases makes them an impractical purchase.

Explanation of Thiele Small Parameters

The use of Thiele Small parameters by manufacturers is so that speaker designers can know the performance of a loudspeaker driver and design the enclosure accordingly for accurate sound reproduction. There are a few key parts to these parameters, so that for both the electrical and mechanical parts of a system can be measured, being able to design the crossover as well as the whole system performance once you place the drivers within an enclosure.

The following explanations are taken with supporting information from loudspeakerbuilder, 2004:

EBP – this is used to give an idea for what type of enclosure would be best for a speaker. A result close to 50 usually indicates a closed box design, whereas closer to 100 usually indicates a vented port enclosure. This is not an absolute as certain enclosure designs can give different results, yet it is an excellent rule of thumb.

Fs – this is the free-air resonance of a speaker, or in simpler terms the frequency that the speaker really wants to fibrate at thanks to its design. What this means in practical terms is that the speaker will be able to move very easily at this frequency and as a result will make the frequency be louder, so to get a flat sound this peak would need to be controlled accordingly.

Power Handling – essentially what power the speaker is rated to be able to handle. If you go over (put more power through the speaker) than this rating, then you risk damaging the speaker or causing it to completely fail.

Qms – the mechanical quality factor the speaker.

Qes – the electrical quality factor the speaker.

Qts – the quality factor for the total system of the speaker (combination of mechanical and electrical).

Qtc – this is the tuning coefficient for a speaker when you place it into an enclosure. The closer the value to 0.707 here the better as this will give you a flat frequency response and provide you with the most accurate sound reproduction.

Vas – this is essentially a measurement of the stiffness of the speaker, as the value is representative of the total volume of air that the speaker can move, when that air is compressed to one cubic meter.

Although there are other values within these, the above tend to be the more common examples used in the industry to allow designers to pick off the shelf speakers and use them in an enclosure of their own design and know what sort of performance you are going to get out of them.

How to Measure and Improve the Quality of Loudspeakers

Measurement of loudspeakers is more simply done thanks to computers these days. The above Thiele-Small parameters can all be calculated with software like DATS V2, 2018. As mentioned above, this allows the designer to get a good understanding of the enclosure you would need to produce for a specific speaker at the start of the process, with the aim to get the best out of the speaker at this stage.

The second part of the process would be to measure and improve the quality of a fully built loudspeaker. This would be where you have already made the decision to purchase a loudspeaker and you now want to be able to get the best performance out of it.

This is done firstly by measuring the frequency response on and off axis to compare the accuracy of the speaker, giving us a relative measure of its efficiency. This is done using a high-quality dB meter, set to a specific weighting curve. The most common here is the dB(A) curve, as this most accurately mirrors human hearing, however dB(C) can also be used as it is practically flat over several octaves, making it useful for subjective measurements, as well as being just as useful as a comparison to human hearing at louder volumes.


Frequency Weightings (2006)

When you measure a speaker at multiple frequencies using bands of pink noise, you can then see how a speaker performs at these frequencies, giving you a plot seen from many of the speakers in the above document. You can do this both on and off axis at multiple set distances to really give a good overall understanding of how the speaker performs both across different frequencies and within the environment you have it in before you start adjusting its output.

At this point, it is all about trying to get what would most likely be a plot for a speaker full of peaks and troughs looking flatter, as this is what will give the “nice” (balanced) sound reproduction. Graphic Equalizers are now coming in many forms. You have the traditional mechanical equalizers or the modern computerised equalizers which have the same bands (often even more with digital) to allow the user to adjust the speaker output. In simple terms, if there is a peak, that frequency band needs to be lowered, likewise a low trough needs to be brought up. There are limitations here. The last thing you want to do is adjust around certain frequencies (mains frequency being an obvious one) that could seriously harm the overall sound quality by increasing reverberation or starting to create standing waves. It is here where more smart equalizers, such as the Behringer DEQ2496, can be immensely useful in the final system as they have the option to generate pink noise themselves and by plugging in a good quality RTA microphone the system can level itself to flat.

Finally, as mentioned above, simply measuring a speaker and adjusting its output with an equalizer is not enough, as you then need to start working out how the speaker will perform in the environment you have it placed in. This is where not only can room design give you random issues with both diffraction and reverberation, yet you start getting into having equal sound dispersion so that everyone gets the same level and quality of sound, not to mention not having phasing issues. However, that is something outside the scope of this paper.



The Physics Classroom (2010) Pitch and Frequency [online]

Available at: 

[Accessed 2nd April 2018]


High and Low Frequency Waves [online image] (2010) The Physics Classroom

Available from:

[Accessed 2nd April 2018]


The Human Ear [online image] (2016) Hearing Link

Available from:

[Accessed 2nd April 2018]


Table of Sound Levels [online image] (2005) Sengpiel Audio

Available from:

[Accessed 2nd April 2018]


Hartley, H. A. (1958). "High fidelity". Audio Design Handbook. New York, New York: Gernsback Library. p. 200.


Sweetwater Sound (2013) PA Speaker Buying Guide [online]

Available at:

[Accessed 2nd April 2018]


Sweetwater Sound Store (n.d) Peavey QW 4F 5600W Dual 15" Passive Speaker [online]

Available at:

[Accessed 2nd April 2018]


Yamaha (2010) BR10, BR12, BR12M, BR15, BR15M Specifications[online]

Available at:

[Accessed 3rd April 2018]


Tannoy (n.d) Reveal 802[online]

Available at:

[Accessed 4th April 2018]


Tannoy Reveal 802 Frequency Response [online image] (2014) Audio Fanzine

Available at:

[Accessed 4th April 2018]


QW4 Frequency Response from official Manual (n.d) [online pdf]

Available at:

[Accessed 4th April 2018]


Edifier Spinnaker Measurements [online image] (2016) Lifewire

Available from:

[Accessed 4th April 2018]


Edifier Spinnaker [online image] (2016) Head-Fi

Available from:

[Accessed 4th April 2018]


Electrostatic Speaker [online image] (2001) How Stuff Works

Available from:

[Accessed 5th April 2018]


Model 11 SPL Plot [online image] (2013) Princeton University

Available from:

[Accessed 5th April 2018]


loudspeakerbuilder (2004) [online]

Original No Longer Available

Recovered through waybackmachine, available here:

[Accessed 6th April 2018]


DATS V2 (2018) Dayton Audio Test System[online]

Available at:

[Accessed 7th April 2018]


Frequency Weightings [online image] (2006) NTi Audio

Available from:

[Accessed 7th April 2018]


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