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 Sound Intensity 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 Hertz 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: Sound Pressure 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 Decibel SPL, or dB SPL. We will spend more time defining decibels 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 amplitude, 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. Basic Sound Engineering PP271 Fall 2011 4 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.