Understanding nature of Audio
Can we see what we hear?
Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound above 20 kHz is ultrasound and is not perceptible by humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges.
What does it mean… what do we do and learn from above information?
Fourier proved that, any signal and hence any sound no matter how complex it is, is actually a sum of many sinusoidal (Like a naturally occurring sine wave) signals of different frequencies and levels (amplitudes).
The mathematical derivation given by him is known as Fourier series and Fourier Transform.
Coming back to audio, when we say a sound of frequency say 100Hz, it means a sound wave oscillating at one frequency 100Hz, meaning it goes up and down 100 times in a second. Refer the image below.
Sine Wave at 100Hz
This is also known as pure tone as it contains just one frequency, meaning the sound pressure (in case of sound coming through air) is rising and falling 100 times in a second smoothly following the sine wave.
Understanding Tonal Aspects of Sound
The sound coming from musical instruments or for that matter by any means you generate sound, even your voice contains many such frequencies with their own different levels superimposed together and hence they are more complex.
To understand this better, lets us try to see, how a 100Hz , 200Hz and 300 Hz sine wave mixed together look like and sound like.
3 Sine Waves at 100, 200 and 300Hz Superimposed together
Now that we see how different waves of unique frequencies when merged together can make richer and more complex sounds which in case of music gives a timbre and characteristic sound to each instrument as the frequencies generated by them are inherent in them because of the difference in construction, shape, size, material and way of playing.
Categorizing Frequencies
From the above sample sounds, it is not difficult to say that the sound from 100Hz sample sounded heavier and resembling to a big instrument like a cello while the 300Hz sample tended towards thinner and more pronounced. That’s how in general frequenecies are divided into 3 main categories which we commonly refer as Bass, Mid & Treble.
Bass refers to the lower frequencies and treble to the higher frequencies where as the middle range is referred as mids, however there is no fine line separating them but typically, any frequency below 500Hz is loosely referred as Bass or low end and from 500 to 3-400Hz is referred as mids and higher ones are referred as Treble or high end.
At this point of time, it is also worthwhile talking about human ears and the way we perceive sound. So far we discussed about the tonal (frequency) aspect of sound and not the loudness aspect. It is important to explore this dimension as well.
Sine Wave Sound at 100Hz
Sine Wave Sound at 200Hz
Sine Wave Sound at 300Hz
Sine Wave Sound at all three harmonics together 100Hz + 200Hz +300Hz
Sine Wave Sound at all 10 harmonics together 100Hz -1000Hz at step of 100Hz
Understanding Loudness & Power of Sound
POWER & LOUDNESS
The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth (deci-) of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used.
Why Decibel?
Human ear are inherently non-linear in nature and we shall learn this in the later part of this lecture. With increasing volume level the sensitivity of the ear decreases. In other words, at lower levels a slight increase in level appears more increase than by same amount at higher levels. This behaviour is mathematically represented by Log scale which has the property that with increasing level the rate of increase keeps decreasing. This is also the precise reason why the Volume Pots (Knobs) are called Log pots which are designed with increasing rate to counter the non-linearity of human ear and hence providing a constant apparent level increase on the turn of the knob.
For the sake of better understanding of wider audience, I’ll try to explain the concept of logarithm as well.
We know that 10 squared is 100, or 102 = 100. This can also be re-written logarithmically as Log (100) = 2. Similary, Log (1) should be 0, because, 100 = 1.
This means that Log (100) is 2 units more than Log (1), now pay atention to the fact that, 100 is 100 times 1 but if you apply log it just shrinks.
Its important to understand this representation of the relation, this is the core concept of logarithm.
Coming back to the Decibel, the relation between decibel and power is given by following relation:
Decibel or DB = 10 x Log (P⁄P’) here P’ is reference power.
This also means that DECIBEL is a RELATIVE measure. It always means Loudness level relative to a certain reference.
After a short lesson on mathematics lets get to business busting some myths…
Case Study: Higher wattage lead to Higher Loudness
A guitarist ready for some rock n roll action is depressed that he has got just a 10w tube amp not rocking enough for the bigger gigs which have started happening these days. Finally he decided to knock it off and go for a double sized 20watter amp. He brings it over to his jam room and craks up the levels, just to add to his frustration, it was only marginally louder. 🙁
What actually has happened is Mr. Mathematics had just rocked harder! 😛
Lets get back to how we defined Decibel – It is 10 times Log (P⁄P’). Here the new amp is 20W and the older one was 10. So our decibel becomes, 10* Log (20⁄10) = 10* Log2 =10 * (0.30) = 3 Decibel. We now know that by doubling the power only 3 Db increase in perceived loudness occurs.
BUSTED MYTH: Doubling Power doubles Loudness!
Frequency Mix/Profile & Loudness
Case Study: His 20W amp is Louder than My 20W, hence Marshall is Louder than Fender!
We have learned that any sound other than pure sine wave is a mixture of low frequencies, some mid frequencies & some high frequencies, often generalised as Bass, Mid & Treble.
Human ear is not uniform when it comes to sensing different frequencies at the same level or same power. Inherently or naturally, human ears are more sensitive to mids, compare it with fact that vocal range or our speech is the middle region of audible frequencies and GOD has designed our ears to be the most sensitive to these frequencies. This also means that a boost in these frequencies will be perceived as very high increase in loudness or even piercing as the ears are most sensitive for middle range of frequencies. This is also the prcise reason why we tend to like HIGH BASS, HIGH TREBLE and LOW MIDS… recall that party beat.
There is indeed an experimental study done by 2 people named Harvey Fletcher and Wilden A. Munson in 1933 which shows and proves this fact.
Fletcher Munson Curve
Just a quick look at this diagrams which is a equal loudness curve shows that for the same loudness level at any level, the mids decibel are the lowest and lower frequencies are highest. Hence this also means that,
…a balanced sound will have a much higher Bass, Slightly lower Treble & lowest Mids.
Lets come back to the case study and explain!
We are talking about a Guitar amplifier and the case is “our Guitarist” is making an assumption that for the same power & type one brand of amplifier sounds louder than other. TWO pretty subtle things are happening here…
1. A guitar is an instrument which has middle range sound, we just learned middle region being the most sensitive to human ears.
2. Also for same power rating and design type of amplifiers, there are always subtle trademark tone shaping “preamp” sections in them
It is because of exactly this, the overall tonality of amps which is governed largely by the preamp in them becomes different, obviously this is the reason why despite having same output power one amp appear louder than the other…. NOTE THAT it just APPEARS louder, actually its NOT!
Don’t judge by what you perceive, each amplifier has its own character an identity an individuality!
Summing it up
In a nutshell, what we learned about the nature of sound is that,
Sound has 2 distinct yet interrelated aspects, one related to its tonal characteristics and has to do with the constituent frequencies and other is related to power and loudness which has to do with the RELATIVE levels of different frequencies. We also learned that human sensory system is non-linear and has SELECTIVE SENSITIVITY to different frequencies is is most sensitive to mid frequencies.
