Chapter 1: Some Basic Definitions

As illustrated by the famous question about the tree falling in the forest, sound is a name we give to the way we perceive a physical event – the variation of air pressure created by the movement of bodies in that airspace. We live in an environment saturated with sounds, true silence is not only rare, it’s non-existent in any environment capable of supporting life! When the level of sound around us becomes sufficiently low, we even become aware of sound produced within our own bodies by the very circulation of blood in our veins and arteries. The human ear is a remarkably precise and responsive measuring device reacting to the sequential variations in air pressure traveling through the air from objects producing them.

Sound: Sounds are produced by moving objects disturbing the air. As an object moves "forward" in the air, it will compress the air immediately in its vicinity, as it moves "backward" it will tend to suck the air molecules with it creating a zone of rarefied air. So sound = alternating zones of air COMPRESSION & RAREFACTION pushing against and sucking at the eardrum (or a microphone diaphragm). The more tightly packed the molecules = more compressed = the greater the movement in the eardrum (or microphone diaphragm) = louder the sound will seem. SO we can measure by measuring variation in Air Pressure.

Figure 1: Compression and Rarefaction (www.synaudcon.com)

Remember, just as you have probably seen demonstrated with waves in water, the actual air molecules don’t move away from the object, but rather vibrate back and forth more or less

Basic Sound Engineering PP271 Fall 2011 1 in place. It is the energy of the vibration that moves away from the object as molecules bump into each other and pass the energy on. In the case of an object in free space, remember also that the pressure variations will radiate away from the vibrating object in all directions – spherically.

Figure 2: Spherical Radiation (www.synaudcon.com)

Simple Scientific Notation: Before we go too much further, this is probably a good place to introduce some very simple conventions for notation. We use the letter “k” (lower case - for “kilo”) to represent a multiplier of 1000, so we can write 16,000 as 16k Hz. Likewise, we use the letter “M” (upper case) to represent a multiplier of 1,000,0001, so 3.7M Hz would be 3,700,000 Hz. The lower case “m” (for “milli”) on the other hand, represents 1/1000, so we could express the time value of .001 seconds as “1 ms” or one millisecond, or the time value of “0.1 second” could be expressed as “100ms”. We also will see the symbol “µ” used as “micro” to represent 1/1000,000, so 1 µs would be one microsecond, or .000001 seconds. We will also use these suffixes often when talking about voltage levels for microphones and other components. For example, “23µv” would be read as “twenty three micro-volts” and would represent .000023 volts, while “23mv” would be read as “twenty three millivolts”, and would represent .023 volts. Sometimes you will see scientific notation looking like this; “2.5 x 10-6” which is read as “two point five times ten to the minus six” – this means that you take the decimal point and move it six places to the left, adding zeros, so “2.5 x 10-6”would be the same as “0.0000025”. If the exponent is positive rather than negative, you take the decimal point in the other direction – to the right, so “2.5 x 106” would be the same as “2,500,000”. Sometimes, you will see the letter “E” or “e” used in place of the “x10” part of the notation, so “2.5e-6” or “2.5E-6” would be the same as “2.5x10-6”. Often, scientific calculators use this notation since they lack the display to show the superscript. Greek letters are used quite commonly in physics and mathematics,

1 The “M” suffix introduces some confusion for many people when we are dealing with computers. That is because we use a term “megabytes” in describing the size of computer memory. There are 1024 bytes in a kilobyte, and 1024 kilobytes in a megabyte, so there are 10242, or 1,048,576 bytes in a megabyte. But, when we describe the size of a hard disk storage device, we use the traditional scientific definition – so a 200 Mbyte drive will not quite hold 200 megabytes of data. That’s part of the reason your shiny new 500 Gig drive shows you have less than 500 Gig available when you plug it in. Basic Sound Engineering PP271 Fall 2011 2 and there are some that we find often in sound. One of the most common is the Greek letter lambda, written as “λ”, which is most often used to represent wavelength.

Figure 3: Levels (www.synaudcon.com)

Sound Pressure Level: We need not consider pressure too small to move eardrums - For young ears in prime condition (16-18 yrs.) convention establishes this as .0002 dynes/cm² (often stated as “microbars”), or .00002 Newtons/meter² (often stated as “Pascals”, or in this case, as 20 micro-Pascals, or 20µPa). This level is referred to as the threshold of hearing. We peg that as the “Zero Level” for the measuring unit we most often use to define sound pressure level, the SPL, or dB SPL. We will spend more time defining more broadly later. There is a truly remarkable range between this established threshold of hearing, and the loudest sounds we hear every day. In terms of absolute pressure measurement, the effective other end of the scale for sound pressure is the point at which the average person begins to feel pain or discomfort as the overriding sensation – that is, the sound that is so loud it just hurts. There is argument about what that level is, but typically it is stated at between 120 dB SPL and 130 dB SPL, with more experienced listeners trending toward the higher value. In terms of actual pressure measurement, this corresponds to about 63 Pascals. This is more than three million times higher than the threshold of hearing. That is about 3,150,000 times higher pressure! You can see that using the actual pressure values would become tedious fairly quickly, even more so if we were to try to use our more familiar pounds per square inch (psi). One Pascal is equivalent to 0.000145038 psi, so the threshold of hearing (20µPa) would be just 0.0000000029 psi, and the threshold of pain at around 63Pa would be around .0091 psi. We’d find ourselves Basic Sound Engineering PP271 Fall 2011 3 dealing with a lot of fractional numbers, and sound pressure meter faces would be pretty cluttered. Of course, we could use scientific notation, and express the threshold of hearing as “2.9e-9 psi”, but it’s still awkward, and the sheer range of numbers we’d have to deal with is daunting. Fortunately, we have the decibel scale, which will turn out to be much easier to use, and ranges from 0 to 130 for the same span of measured pressures.

Frequency: Number of complete cycles of movement of the object producing the sound each second. A cycle is the complete movement of the object from rest, through the maximum positive movement back through the original position, to the maximum negative movement and back to the original position again. Unit of measure is the Hertz, one Hertz(Hz.) is one complete cycle per second. It is capitalized because it is named after the physicist Heinrich Hertz, whose research in the 19th century established the existence of both the photoelectric effect and electromagnetic waves in the UHF and VHF ranges.

Frequency Range: The span of frequencies that an instrument or piece of equipment is capable of producing. For instance, if a Piano's lowest frequency key was at A0 (27.5 Hz), and it's highest key was at C8 (4186.01 Hz), we would describe its frequency range as "27.5 Hz to 4186.01 Hz". Note that this says nothing about the , or volume of the sounds produced, only the possible range of the frequencies covered.

Wavelength: As our moving object compresses the air molecules, it also imparts movement to them, in fact we can think of the movement in the same way we think of waves moving out from a dropped Figure 4: Wave Definitions pebble in a pond. As the molecules bump against each other, each one "jostles" the next into a small displacement, which causes it to hit the next and so on. Just as in the water, where the water doesn't actually move much, the individual molecules don't take off for parts unknown, but the compression zone does travel away from the moving object. Since frequency was a measure of the movement of the object with respect to time, if we know the velocity of sound in the air (that is, how fast sound gets from one place to another), we could figure out the physical distance covered by one complete cycle of the sound "wave". In the same way that we know that if we are going 50 miles per hour, and travel for ½ hour, we will cover 25 miles (50/2=25) we can use the formula.

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Wavelength = Speed of sound / frequency

Velocity Or " = frequency and, since the speed of sound at room temperature at sea level is about 1130 ft/sec, for a 50- Hz tone we have a wavelength of

! 1130 ft /second " = 50Hz

or 22.6 feet. That’s pretty long for just one wave! If you do the same calculation for 20 Hz, you’ll discover! that a single wave at that frequency is over 56 feet long. As we’ll see, this has serious implications when we are working in spaces that are often fractions of that length. But, also notice what happens at the other end of the frequency spectrum – a 16,000 Hertz tone would have a wavelength of just 0.07 feet, or a little over ¾ inch.

One ms= 1 foot rule: The speed of sound in air will come back into our discussions frequently, and this is a good place to introduce one of the really convenient rules of thumb that we will find essential to live sound engineering. It takes time for sound to get from one point to another. We are often needing to calculate how long it takes a sound to get from one place to another, for instance, how long it takes for the direct sound from a vocalist to reach an audience member, compared with how long it takes for a reflection of that sound to reach the same audience member, or how long it takes for the sound from the vocal speaker to reach the audience member. It is our great good fortune that the speed of sound in air at room temperature (and at sea-level) is roughly 1130 feet per second. So, if sound travels about 1130 feet each second, in 1/1000 of a second it travels 1.13 feet. While it is good to remember that extra 0.13 feet per second, for practical purposes when we are dealing with short distances, we can just remember that sound travels about a foot each millisecond. So, if you know you are 12 feet from that singer, you know it will take about 12ms for the direct sound from her voice to reach you. And, if you know that the speaker carrying her voice is 20 feet from you, then you know that it will take about 20ms for that sound to reach you, thus you know that the sound from the speaker will hit you about 8ms later than the sound from the vocalist. As we’ll see later, that is very valuable information, and being able to know it at a glance is really useful.

Wavelength in other media: Since wavelength is determined by the speed of propagation in the medium and the frequency, note that it is different in different media. For example, the speed of sound in pure water is about 4908 ft/sec (Water is much less compressible than air, so it follows that the pressure variations would travel faster). Using our examples from before, a 50Hz wave in water would have a length of 98.16 feet, compared to the relatively short 22.6 feet in air. Likewise, our 16K Hz wave would have a length of more than 3-1/2 inches, as opposed to ¾ inch in air. So, obviously, the design of speakers and microphones for use in water would be quite different from those used in air.

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Ok, but what about the speed of sound in wires, after it is converted into electrical impulses? We know that the speed of electron propagation in wire approaches the speed of light. Using a conservative 70% of the speed of light, we have a speed of 0.7 x 186,000 miles/second, or 130,200 miles per second. So, using our wavelength formula, we find the wavelength of a 50Hz wave to be 2,604 miles! The wavelength of our 16K Hz tone is still 8.13 miles! So, who cares? Well, you might if you want to avoid being the victim of audio serpent lubrication (snake-oil2) salesmen selling expensive wire. One of the claims made for some very widely advertised wire products is based on what they claim to be the science of transmission-line theory, and something called “skin-effect”. As it turns out, this is a very real phenomenon at radio frequencies, but it is utterly meaningless at audio frequencies. In order for a wire to be considered long enough to exhibit this effect, it must be at least as long as the shortest wavelength of the signal of interest. So, if you routinely use speaker cables that are more than 8 miles long, then this effect might be important. But since most of you would rarely use cable longer than about 30’ in a home installation, and rarely longer than 200’ in a professional venue, you can probably safely ignore skin-effect and when someone talks to you about “transmission-lines” in this context you can assume they are full of something other than expertise. We politely refer to such claims as “marketing- based science”.

Figure 5: Front and Rear Radiation

2 The term snake-oil salesman as an archetype of the dishonest perpetrator of hoax has a fascinating derivation with a surprising factual background. Originally the fats and oils harvested from the Chinese Water Snake were quite effective for joint pain relief. But, when American patent medicine salesmen encountered Chinese railroad workers selling the stuff, they ridiculed it as inferior to their own panacea products. So the term as derogative actually grew out of efforts to eliminate competition for an even more dishonest product! Basic Sound Engineering PP271 Fall 2011 6

Phase: Note: when our object moved forward it compressed the air in front creating what we think of as a "positive" sound pulse. Simultaneously, the object creates a partial vacuum or area of reduced pressure behind it, which we consider a "negative" sound pulse (compared to the front pulse). For each pulse from the front, there is an equal and opposite pulse from the rear. The timing relationship between the signals is called the Phase Relationship, (or Coherence) and in this case the signals are said to be 180 degrees out of phase. Phase will be a crucial concept to us later on in the class, and is very important to the sound engineer. If we could put a microphone on each side of the object as in the illustration above, and make a recording of both sound waves, then play them back together, they would cancel each other out, as for every positive portion of the front wave, there would be a negative portion of the back wave of equal energy. If, on the other hand, we were to invert the signal from the rear microphone – reverse it’s polarity – the resulting electrical signal would be identical to the one from the front microphone and instead of canceling out, the two signals would add together resulting in a combined signal twice as loud.

The two microphones do not need to be on opposite sides of the source to see this effect at work. If we set up two “identical” microphones next to each other and a fixed distance from a sound source, then start to move one microphone relative to the other, we will hear the effect of phase shifting as the two signals combine in different ways. When we get the second microphone to be exactly ½ wavelength away from the first, we should hear nearly complete cancellation (the nearly part is due to the fact that there is more than one path for sound to get from the source to the microphones). The graph below shows three different positions along this continuum. Note that this phase shift can result from any number of causes, ranging from physical microphone position to electronic delay in signal paths due to processing.

Figure 6: Phase and Summation

Polarity: When you physically reverse the leads on a speaker or on a microphone – switch the two signal wires around - it is fairly obvious that you will also “flip” the signal curve – where you had a positive pulse you’ll now have a negative pulse, and vice versa. This

Basic Sound Engineering PP271 Fall 2011 7 actually looks very much like a 180° phase mismatch, and you will often hear people refer to it as “reversing phase”. It is important to make a distinction between polarity reversal and phase shifts though, because a phase shift always involves a change in time – it is a result of the signal arriving later or earlier due to some intervening medium, When you reverse polarity, there is no time shift – the resulting signal is simply flipped over in place.

Superposition: Figure 6 illustrates another important concept to bear in mind as you think about the way audio signals work. When two sound pressure waves, or electrical signals within a piece of equipment are combined, they “superpose” – that is to say, the resultant pressure or electrical signal is the mathematical addition of the two original signals. In Figure 6, you can see that by looking at the bottom waveform, which is the mathematical combination of the two waves above it. The waves shown in Figure 6 are quite simple, so the resulting wave is also simple. If you go into an audio editor like Logic or Reaper, and zoom in on a sound waveform, you can see this same kind of superposition in action when you bounce several tracks down to a combined track.

Dynamic Range: The span between the quietest and loudest sounds an instrument can produce is its dynamic range. Note there is no mention of frequency, this is only a measure of amplitude or "". The dynamic range of a harpsichord is nearly zero, because the strings are always plucked at the same force, giving the same loudness whatever the playing style. The voice, on the other hand, having a lower frequency range than the harpsichord, nevertheless has a much broader dynamic range, from a whisper to a shout.

Figure 7: Sound and Signal Level Relationships

We can speak of dynamic range in terms of either sound pressure or in terms of electrical levels. The chart above relates a number of terms that we will visit during the first few weeks of the course. Don’t be put off by the apparent complexity, or the number of terms. You will discover that all these interrelate in a way that will make more sense as we go along. Basic Sound Engineering PP271 Fall 2011 8

DECIBEL: Remember Decibel = ratio It is possible to spend weeks engaged in discussion about the correct and incorrect application of the term decibel. We will avoid the temptation. In the early days of installing the telegraph networks in the UK and the US, engineers needed a way to quantify the expended to push a signal through the wires. They came up with a measure called the “Mile Standard Cable” (MSC), which compared power levels at both ends of a mile long 19 gauge open cable. Renamed for Alexander Graham Bell in 1929, the measure was defined as:

(n)Bel = log(W1/W0)

Where “W0” is the reference Power, “W1” is the power to be compared to the reference, and “n” is the resulting number of Bels. Notice that this number expresses a ratio of the two powers being compared. As it turns out, a more useful expression is one tenth of a Bel, which became the “decibel” or “dB”, and the formula is restated as:

(n)dB = 10*log(W1/W0)

NOTE: this is a POWER measurement - we can use it in comparing (), or in comparing total ACOUSTIC POWER at a source - i.e. at a speaker Commonly the term dB PWL or more simply LW is used here so we would have

LW = dB PWL = 10*log(W1/W0) EXAMPLE: we have a 100- amp hooked to a speaker and we replace the 100 watt amp with a 200-watt amp - what is the power increase expressed in db pwl?

LW = dB PWL = 10*log (200W/100W) LW = 10*log(2) = 3.01 dB

So, when we doubled the power, we got about a 3 dB increase – this is an important rule to keep in mind for system design.

Power is often defined broadly as the rate of doing work. More precisely, it is the rate at which energy is supplied to a system or consumed by a load. A frequent error made when discussing audio is to confuse Power with Intensity. Intensity is a measure of power expended within a specific area, and is usually measured in Watts per square meter. Intensity measurements are usually represented by the letter L with a subscript of “I” instead of “W” (LI). Sound Intensity calculations use the same formlua as measurements, with the substitution of intensity for power. There is a reference level that is related to the intensity needed to cross the threshold of hearing – the pressure per unit area that would be enough to move the eardrum. That reference level is 10-12 Watts/M2. So, an intensity calculation would look like this:

(n)LI = 10*log(I1/I0)

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-12 2 Where “n” is the number of dB Intensity, “I0” is the reference of 10 Watts/M , and “I1” is the measured value that is being compared to the reference. Sound intensity measurements are not commonly used in system design, but they may be encounterd from time to time. It is important to avoid using the word “intensity” when describing other phenomena in audio measurement. By far the most common measurement you will encounter in describing sound fields is Sound Pressure Level (SPL). This is the unit that most direct reading sound meters report, and the measure that most logically tracks the way we actually hear. As we noted above, there is a defined “0” reference level for sound pressure of 20µPascals (.00002 Pa). Comparisons of two sound pressure levels can be made with a similar formlua, however because of the way that pressure and power are related, the multiplier changes from 10 to 20. The letter Lp is often used for sound pressure. So, the formula looks like this:

Lp = (n)dB SPL = 20*log(p1/p0)

Where “n” is the number of deciBels, “SPL” is the suffix that defines this as a sound pressure level measurement, “p1“ is the measured pressure, and “p0“ is the reference pressure, usually 20µPa.

Example: the neighborhood physicist tells us that he measures the sound pressure from our boom-box as 200 dynes/cm2. What is the sound pressure in dB SPL? Remember 0 ref. = t.o.h. = .0002 dynes/cm2 (this is the same as our 20µPa) So Lp = 20*log(200/.0002) = 20*log(1000000) = 20*6 = 120 dB SPL

Some boom-box !!!! (And some geeky neighbor!) We agree to turn it down to 100 dynes/cm2, how many dB did we turn it down and what is the new level? Change in db = 20*log(100/200) = 20*(-3) = -6 db New level = 20*log(100/.0002) = 20*(5.69) = 114 db spl

Note: we could simply have subtracted the 6 db from the 120 db for the answer. Note: cutting the actual pressure by 1/2 only resulted in a 6db drop.

So, one of the real advantages of using the deciBel becomes clear in this example. As long as we know the reference is the same, we can simply add and subtract deciBel changes to get new levels. Another advantage relates to the fact that our hearing responds to sound pressure in the same “logarithmic” way. For most people with good hearing, a 1dB SPL change in sound pressure is just perceptable, and a 3dB change is audible by most people. Roughly a 10dB change is perceived by most people as about “twice as loud” or “half as loud”. The really, really good news is, we can use a sound pressure meter that is calibrated in dB SPL, so we can ignore all the Pascals, dynes, and Newton Meters, and just work in SPL

Basic Sound Engineering PP271 Fall 2011 10 directly. So, if we take a measurement of 96dB SPL, and then change the system output so the level drops to 93dB SPL, we can just say that there was a 3dB SPL drop.

So far, we have been mostly talking about measuring sound – but we can use the deciBel for electrical measurments as well. The thing that confuses people is keeping the reference level straight. There are some commonly used suffixes that define those reference levels, but frequently these are misused or misunderstood. With the exception of dB SPL, which is universally understood to have the 20µPa reference, the best practice is to explicitly state the reference at least once in any document. I will note the common and the correct notation here, but will use the correct notation as often as possible. While you may find the IEC notation a bit cumbersome at first, it has the advantage of plainly stating the reference in every use of the term, thus eliminating the confusion. That confusion was the norm before the standard is clear, in fact, there are different uses of the term dBu in audio and in broadcast engineering. Strangely, the standards are resisted by many pros, perhaps it’s just that we have finally gotten used to the alphabet soup of dB notations, and don’t relish a change. Since the standard requires the reference to be plainly stated, either with every cite, or every time that a reference is changed within a given document, the confusion is greatly reduced. dBm - The dBm is a measure of electrical POWER(10*log), and the 0 dBm level is defined as 1 milliWatt (.001 Watt). The correct notation according to IEC is as follows -36 dB (ref 1 mW), or shortened to 36 dB (1 mW). THIS IS NOT a VOLTAGE REFERENCE !!!!!! If someone asks how many volts are indicated by a 20 dBm signal - YOU DON'T KNOW, unless the impedance of the circuit is listed !!! IF the impedance is 600 , then and only then the voltage at 0dBm will be .775 volts. dBu or dBv - this has a 0 reference of .775 volts REGARDLESS of IMPEDANCE and is a MEASURE of VOLTAGE (20*log) The correct notation is -36 dB (ref 0.775vrms), or 36dB(0.775vrms).

Example: An amp’s output is +20 db (0.775vrms) - this says that the output voltage is found by 20 db(ref 0.775vrms) = 20*log(V/.775v) which we can work out to be 7.75 volts

NOTE: there is a simple way to solve for the voltage when the dB difference is known: For VOLTAGE (or Sound Pressure) 6 dB increase = double voltage 20 dB increase = 10 x voltage 40 dB increase = 100 x voltage 60 db increase = 1000 x voltage

SO in the last example 20 dBu would correspond to 10 x 0dBu, or 10 x .775 volts = 7.75 volts

Basic Sound Engineering PP271 Fall 2011 11 dBV (note capV) - This is almost the same as dBu, but uses 1 volt as the 0 dBV reference, which makes the math easier. We can convert dBV to dBu by simply adding 2.2 dB to the dBV value for comparison purposes. Once again, the correct notation for this would be -36 dB (ref 1.0vrms) or -36 dB (1.0 vrms)

Example: A microphone is listed as having an open-circuit sensitivity Of -66 dBV - say what? The microphone's output is 66 db lower than the 0 dBV reference of 1v or: -66 = 20*log(V/1) -3.3 = log (V) .0005 volts = V Of course, this could also be stated as 500µv, or 0.5mv Another solution would be to note that -60db is .001 (one one thousandth of the ref), and the other -6 db would be .001/2 = .0005 volts

Decibel Calculation Reference chart Quantity Reference & Unit Symbol Formula 2 SOUND PRESSURE .0002 dyne/cm dB SPL or LP 20*log (p1/p0) .00002 N/m2 20 µPascals -16 2 SOUND INTENSITY 10 W/cm LI 10*log (W1/W0) 10-12 W/m2 actually figures are Watts/unit area -12 SOUND POWER 10 W or dB PWL or LW 10*log (W1/W0) 10-13 W -3 10 W(milli-Watt) dBm dB (1 mW) 10*log (W1/W0)

VOLTAGE 0.775 Volt dBu ,dBv) 20*log (E1/E0) [dB(0.775vrms)]

VOLTAGE 1 Volt dBV dB(1.0vrms) 20*log (E1/E0) NOTE: for Voltage and Sound PRESSURE (20*log formula) +6 dB change = 2 x original -6 dB change = 1/2 original +20 dB change = 10 x original -20 dB change = original ÷ 10 +40 dB change = 100 x original -40 dB change = original ÷ 100 For POWER Measures (10*log formula) +3 dB change = 2 x original -3 dB change = 1/2 original +10 dB change = 10 x original -10 dB change = original ÷ 10 +20 dB change = 100 x original -20 dB change = original ÷ 100

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Measurement Devices: We have noted the SPL Meter, which reads directly in dB SPL. These consist of a microphone and a circuit that converts the pressure appearing at the mic to an electrical signal, then quantifies that signal and displays the result. Usually, a Sound Pressure Meter will have multiple ranges, and it may have either an analog or digital display. They range in cost from around $40 for a cheapo Radio Shack meter, to thousands for much more precise instruments which often are combined with other functions. In order for the measurement of such a meter to be reliable, regular calibration is required, and for most serious measurements, the engineer will use a calibrator to confirm the accuracy of the meter for each use. Because the human ear does not register all frequencies equally, SPL meters generally have at least two selectable weighting curves, “C” and “A”, and more expensive meters will also have a “B” weighting scale. The graph in figure 8 shows how the weighting curves affect the portion of the frequency spectrum that is being measured.

Figure 8: Weighting Curves for Measuring Sound Levels (courtesy www.synaudcon.com)

The “A” weighting scale simulates the way our ears work at low sound pressure levels, so is frequently used to measure the effects of noise on workers or others in an environment. The “B” weighting scale simulates the frequency response of our ears at somewhat higher levels (around 70dB SPL), and it is not often used. Many inexpensive meters will not include a B weighting scale. The “C” weighting scale simulates human hearing at higher levels, 90dB SPL and above. It will capture more low frequency noise (or sound) and so it is better at indicating the true level of noise in an environment. When measuring music, an A weighted reading will almost always be lower than a C weighted reading. The good news for sound engineers is that almost all statutes that regulate the maximum sound pressure level permissable in an event are stated as A- weighted measurements. Basic Sound Engineering PP271 Fall 2011 13

In addition to weighting, SPL meters usually will have a switch to select “Fast” or “Slow”. These control how long the measurement “holds” in the meter, with the Fast setting able to capture transient sounds more accrately, while the Slow setting shows a more “averaged” reading, which corresponds a bit better to the way we perceive the level of sound. Even relatively inexpensive meters will often have a “Max Hold” function that allows the meter to hold the highest level that it records in a session. Please notice something interesting about the graph in figure 8. The x-axis is not a perfectly linear scale – that is you will see that the scale changes as you move from left to right. This is a Log-Scale, and it corresponds to the way we perceive frequencies. For example, there is about the same physical distance on the scale between 50 and 100 Hz as there is between 500 and 1000 Hz. Musicians in the class will immediately identify how these two spans are similar – they both comprise an octave spread, that is they represent a doubling of frequency. We think of the audible spectrum as divided into octaves, with each succeeding octive containing twice as many discrete frequencies as the last. So, there would be an octave span between 50Hz and 100Hz, another between 100Hz and 200Hz, another between 200Hz and 400Hz, and so on. As it happens, our hearing works in a similar logrithmic way – that is, we tend to perceive each of these progressively larger spans as “equal” in breadth. So, drawing our graph with a log scale on the x-axis allows us to see a straight line across the graph (a “flat” line) as an indication of a signal that has equal level across all octaves.

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Figure 9: ISO Standard Octave and 1/3 Octave Frequency Divisions (courtesy www.synaudcon.com)

The graph in figure 8 illustrates another kind of meter, the Spectrum Analyzer. A Spectrum Analizer, sometimes called a “Real-time Spectrum Analyzer” or RTA, is similar to an SPL meter in that it uses a microphone for input, but unlike the SPL meter, it splits the resulting signal into individual portions of the spectrum and indicates the level at each of those spectra. The number of splits varies from unit to unit, with typical ranges including 1 octave, 1/3 octave, and sometimes 1/6 octave. The RTA gives us a display like that of figure 8 that varies in real time as the sound field changes, it gives us a sort of instantaneous snap-shot of the frequency content at the position of the microphone. The RTA is most useful if we can generate a predictable signal into the system and play it in the room, so we can compare what the microphone “hears” to what we know the signal was supposed to be. There are a number of different types of signals that are used for this, but the most common are white noise and pink noise. White Noise: White noise is analogous to white light, which is light composed of all colors, in that White noise contains equal energy at all frequencies. Since each successive octave contains twice as many discrete frequencies as the last, it will also have twice as much white noise energy as the last one. Thus it will contain 3 dB more sound level than the last, and a log graph of level vs. frequency will rise at the rate of 3 dB per octave. This is why white noise sounds "hissy". Basic Sound Engineering PP271 Fall 2011 15

Pink Noise: Not an English band, but rather treated white noise, with a filter applied to reduce the level by a rate of 3 dB per octave, giving us equal energy per octave. This makes a very useful tool as a log graph of pink noise level vs. frequency is a straight or "flat" line. This is the noise that sounds like a jet taking off that you hear during sound system tuning for concerts. Figures 10 and 11 show White and Pink Noise 1/3 Octave Spectrum Analyzer Displays.

Figure10: White Noise 1/3 Octave RTA Display

Figure 11: Pink Noise 1/3 Octave RTA Display Basic Sound Engineering PP271 Fall 2011 16

Figures 12-14 demonstrate A, B, and C weighting applied to pink noise plots.

Figure 12: Pink Noise 1/6 Octave Display, A Weighting Filter Applied

Figure 13: Pink Noise 1/6 Octave Display, B Weighting Filter Applied

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Figure 14: Pink Noise 1/6 Octave Display, C Weighting Filter Applied

In all the displays, you will notice some irregularity in the levels – this is a normal artifact of the way the broadband noise signals are produced. The variations are random, and over time average out. Some measurement systems actually take multiple measurements and average them in order to improve the uniformity of the measurement.

Loudness and Audibility: While we are talking about perception of audio, we should take a look at the subject of audibility. Research done in the 1930’s by a number of scientists established that it takes a different “threshold” of sound pressure level for tones of different frequencies to become audible. Most often cited in this research are Harvey Fletcher and W. A. Munson, who established the Equal Loudness Curves in 1933. These curves are now commonly called “Fletcher-Munson” curves, though they have been refined by numerous researchers since the early work. They are based on studies in which large numbers of people are sampled and their responses averaged. 1000 HZ is taken as the baseline (because it is one of the frequencies that we hear best), and a tone is played at 1000 Hz at a defined amplitude, then another tone at a different frequency is played and adjusted until the respondent reports it is at an equal level to the 1K Hz tone (sounds just as loud). Then, the 1K HZ tone is played at a different amplitude, and the process is repeated. After doing this with large numbers of subjects for a range of levels, a set of curves can be established which define the equal loudness at different amplitude levels. The curves are called Loudness Level curves, with the units referred to as “Phons”.

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Figure 15:Equal Loudness Contours (courtesy www.synaudcon.com)

These curves are very instructive in terms of system design. First, it is clear from the curves that it takes a lot more energy at the low end of the spectrum to produce sound that will be perceived as equal in level to the sound at the 1K-2K range. As well, looking at the shape of the curves, it is clear that the lower in amplitude we go, the more pronounced is this difference. In other words, if you are shooting for a 100dB SPL average level, there is less difference between, say the level that you will need at 100 Hz and the level you will need at 1K Hz than there is if you are working down around 60 dB SPL. Also, it shows you that there is a distinct bump in our hearing ability at around 2800-3200 Hz, so it is likely this is an important frequency range for some reason. Finally, notice that these curves are more or less the inverse of the A weighting curve we discovered above. This should be no surprise, the A, B, and C Weighting curves were, of course, designed in response to the equal loudness discoveries.

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Figure 16: The Structures of the Human Ear (courtesy www.synaudcon.com)

Finally, a nod to the most important instrument you will ever own when it comes to understanding and manipulating sound. The human hearing apparatus is a complex and somewhat mysterious mechanism that is the final arbiter in any discussion of how good a system sounds, or what sounds good. The frequency curves shown below the ear structure are measurements at two different frequencies by small microphones placed in the ear canal, so that they are showing how the Pinna (sometimes Pinnae, sometimes “floppy part”) of the ear has an impact on what we hear. The sharp notch at around 1K HZ is actually a result of sound reflections off of the shoulder mixing with the direct sound and canceling out at the frequencies measured (we’ll see more about this on a larger scale in chapter two). The shift in response at different frequencies caused by the Pinna play a part in our ability to locate sounds in the vertical direction.

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Hearing damage is an unfortunate liability in working with sound. Ear buds on iPods and other personal stereo systems introduce the possibility of extremely high listening levels that may permanently damage hearing. Likewise, mixing extremely loud shows or working in loud environments can lead to damage that is irrecoverable, including both threshold- shift (inability to hear low level sounds) and more insidious problems such as tinnitus. Even without exposure to repetitive loud sounds, everyone’s hearing degrades with age. Humans reach their peak for hearing acuity at around 18 years of age, it is literally downhill from there. High frequencies are the first to go, partly because of the structure of the inner ear. In males, by the time one is in their late 20’s they have already lost significant acuity, females tend to lose their acuity at a somewhat slower rate than males. In order to reduce the rate of loss, the sound professional is well advised to be meticulous about wearing hearing protection in loud environments, avoiding prolonged exposure to extremely high levels, and generally taking good care of instruments that mean so much to their livelihood.

We will come back to the terms we’ve defined in this chapter fairly frequently as we go forward. An important thing to keep in mind as you study any type of science or engineering is that you don’t really have to remember everything that you study as you go forward. You will find that the terms and formulae that you use regularly will remain with you, but that some of the more obscure information won’t. Science isn’t about memorizing details it is about developing a technique, and remembering how to find the details when you need them. So, think of the information in this chapter, and in the rest of this text, as a ready reference. When you need to, flip back and look up the information. You will notice that when I am teaching, I often will go back to a resource before answering a question – there is too much to remember and not enough memory to hold it all – needing to look up a detail is no fault. That said, there are some frequently used relationships that are worth committing to memory. From this chapter, I suggest that you try to commit the decibel relationships for 3, 6, 10 and 20dB along with the basic formula for calculating decibel differences for both voltage and power to memory, as they will serve you well. Also, the 1 foot = 1ms rule for sound arrival is something every sound person should commit to memory.

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