Introduction to Computer Music: Volume One

6. What is Amplitude? | page 3

Power and Intensity

Power is a measurement of amplitude over time. The RMS measurement from the previous page is averaging the fluctuating amplitude over time, and is therefore an excellent measurement for electrical and acoustic power (you may see speaker or amplifier ratings in rms power in watts, meaning the continuous amount of power they can either receive or generate).

The unit of measurement for power is the watt, named after James Watt.
1 watt = 1 newton (N) of work or energy transferred per second*

Power does not change with distance (i.e. whether you view light from an 80-watt light bulb from the moon, or place your eyeball on it, it's still 80 watts). A sound power level is a measurement of the total power generated by a sound source radiated in all directions.

The power of the original sound source, along with distance of measurement from the sound source or the energy passing through a specific area (such as a square meter) perpendicular to the sound source, combine to form the intensity. Intensity (I) is referred to as a "sound field quantity" as opposed to the "power field" quantity above (apparently sound field quantity is now too old skool and should be replaced by root-power quantity (like rms on the preceding page), but your author is old skool so it stays.

The common unit of measurement for intensity is watts per meter2 (or W/m2).

Intensity can be seen as amplitude over time over an area. As the surface area of the sound sphere expands, the amount of energy generated by the sound source is distributed over an exponentially increasing surface area. The amount of energy in any given square meter of the expanding sphere's surface decreases exponentially by the inverse square law, which states that the energy drops off by 1/distance2. So acoustic energy twice the distance from the source is spread over four times the area and therefore has one-fourth the intensity. Simply put, relative intensity is the reciprocal of the change in distance squared (1/d2). For acoustic sounds, the intensity values in W/m2 can be extremely small. In fact, the threshold of discomfort is a whopping 1 W/m2, a vacuum cleaner (what's that?) at 1 meter produces about 0.00001 W/m2 .

The inverse square law is extremely useful to remember in microphone placement, where even small changes in distance can have a significant impact on the resultant signal strength.

You may recall from your grade-school math that the , so as the radius of a sound sphere increases arithmetically, its surface area increases geometrically. The intensity of the source signal energy is distributed over the broadening surface area so that the , where s = the source intensity.

Sound pressure level (or SPL), another sound field quantity, is an extremely useful measurement for acoustic study and recording and is frequently used to measure at the point of perception (i.e. the listener) or the placement of a microphone. It is a comparative measure of the relationship between a sound pressure (actually the rms of sound pressure amplitude) at a certain distance to a reference value for the threshold of human hearing, which is usually 0.00002 pascals (20 micropascals, or 20μPa), often described as the sound of a mosquito at 3 meters. SPL measurements without mention of distance, except for ambient sounds (for example a quiet room) are not often useful. SPL is normally expressed as a decibel value, and specifically labeled [dB SPL]. 0 dB SPL corresponds to the threshold of hearing. The formula for computing is on next page. A chart of common sounds also follows, but it might be fun to mention here that a stun grenade at close distance, should you experience it, can produce a deafening 158-172 dB SPL. The correlation between sound pressure in pascals and dB SPL can range from 0.00002 Pa=>0 dB SPL to 200 Pa=>140 dB SPL and beyond. While labeling is not always accurate, a quality labeled dB without the SPL will usually refer to power or intensity, not sound pressure.

A few more relationships between amplitude, intensity and power: intensity is proportional to the square of the amplitude. So if the amplitude of a sound is doubled, its intensity is quadrupled. Power is also proportional to amplitude squared. Therefore, power and intensity are proportional to each other. For an excellent chart relating dB SPL, amplitude as Pa, and intensity(I) as W/m2, click here.

Putting it all together

Term Property Unit of Measurement
amplitude Amplitude is the energy of a sound wave present, or the magnitude of maximum disturbance of the medium (air in our case), during one cycle of a periodic wave, known as peak deviation. pascals, or newtons per square meter (N/m2)
power Power is the rate at which energy is being produced or used. In acoustics, this translates into amplitude over time. watt (also related is rms and SPL)
intensity Intensity is the power present over an area, such as the outer surface of an expanding sound sphere. So from the top, intensity is the amplitude over time over an area. watts per square meter (W/m2)

*An energy transfer of one watt per second is equivalent to a Joule, a common measurement in electrical power. The power of one Joule per second is a watt. So a Joule is a measurement of energy, and a watt is a measurement of power. These terms are frequently, but mistakenly, used as synonyms. Is it all clear now?

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