# Chapter One: An Acoustics Primer

#### 7. What is amplitude? | Page 3

Power and Intensity

Power is a measurement of amplitude over time.

The unit of measurement for power is the watt (W), 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 power is still 80 watts). A sound power level is a measurement of the total power generated by a sound source radiated in all directions.

RMS power: The RMS measurement from the previous page is averaging the fluctuating amplitude over time, but is a somewhat controversial and often misused measurement for electrical and acoustic power. When used, it is typically measured into a resistive load or acoustic impedance for a fixed period of time. You may see published speaker or amplifier ratings in rms power in watts, meaning the maximum continuous average power they can either receive or generate via sine wave at minimal distortion into a resistive load of 4 or 8 ohms for a period of one minute without frying (resistance causes heat), as has been determined by government standards. Peak power differs from rms power in that it is the maximum non-averaged power a unit can output in a short burst, normally a much higher value, and some dishonest amp manufacturers used it deceptively implying it to be RMS power until the FTC put a stop to it. You may also see the specification PAPR, which is the peak-to-average-power-ratio.

Intensity: 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 or root-power quantity (similar to rms on the preceding page).

The unit of measurement for intensity is watts per meter2 (or W/m2).
Intensity can be characterized 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 . Therefore 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 or .

For acoustic sounds, the intensity values in W/m2 can be extremely small. In fact, while 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 . ##### INVERSE SQUARE LAW

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. The image above shows each doubling of distance exponentially reduces a sound's intensity at any given point, and that four times the distance will yield only 1/16th the intensity at a particular microphone's diaphragm location. ##### SOUND SPHERE MATH 101

You may recall from your grade-school math that the surface area of a sphere equals 4πr2, 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 Sound Pressure Level (SPL)

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 at a certain distance (actually the rms of sound pressure amplitude) 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 correlation between sound pressure in pascals and dB SPL can range from 0.00002 Pa, which equals 0 dB SPL to 200 Pa which equals 140 dB SPL and beyond. The formulas for computing various forms of decibels are on following page.

While labeling is not always accurate, a sound quantity 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 the square of the amplitude.
Therefore, power and intensity are proportional to each other.

For a chart of common sounds relating dB SPL, amplitude as Pa, and intensity(I ) as W/m2, see this page.

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)

Mini-Factoid: 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.

*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.