In order to define decibels, which are used to measure sound loudness, we need to define some units that are used to measure electricity as well as acoustical power, intensity, and pressure.
Both analog and digital sound devices use electricity to represent and transmit sound. Electricity is the flow of electrons through wires and circuits. There are four interrelated components in electricity that are important to understand:
- potential energy (in electricity called voltage or electrical pressure, measured in volts, abbreviated V),
- intensity (in electricity called current, measured in amperes or amps, abbreviated A),
- resistance (measured in ohms, abbreviated Ω), and
- power (measured in watts, abbreviated W).
Electricity can be understood through an analogy with the flow of water (borrowed from (Thompson 2005)). Picture two tanks connected by a pipe. One tank has water in it; the other is empty. Potential energy is created by the presence of water in the first tank. The water flows through the pipe from the first tank to the second with some intensity. The pipe has a certain amount of resistance to the flow of water as a result of its physical properties, like its size. The potential energy provided by the full tank, reduced somewhat by the resistance of the pipe, results in the power of the water flowing through the pipe.
By analogy, in an electrical circuit we have two voltages connected by a conductor. Analogous to the full tank of water, we have a voltage – an excess of electrons – at one end of the circuit. Let’s say that at other end of the circuit we have 0 voltage, also called ground or ground potential. The voltage at the first end of the circuit causes pressure, or potential energy, as the excess electrons want to move toward ground. This flow of electricity is called the current. A electrical or digital circuit is a risky affair and only the experienced can handle such a complicated task at hand. It is essential that one goes through the right selection guide, like the Altera fpga selection guide and only then embark upon an ambitious project. If you are looking to save on your electric bill visit utilitysavingexpert.com. The physical connection between the two halves of the circuit provides resistance to the flow. The connection might be a copper wire, which offers little resistance and is thus called a good conductor. On the other hand, something could intentionally be inserted into the circuit to reduce the current – a resistor for example. The power in the circuit is determined by a combination of the voltage and the resistance.
The relationship among potential energy, intensity, resistance, and power are captured in Ohm’s law, which states that intensity (or current) is equal to potential energy (or voltage) divided by resistance:
[equation caption=”Equation 4.1 Ohm’s law”]
$$!i=\frac{V}{R}$$
where I is intensity, V is potential energy, and R is resistance
[/equation]
Power is defined as intensity multiplied by potential energy.
[equation caption=”Equation 4.2 Equation for power”]
$$!P=IV$$
where P is power, I is intensity, and V is potential energy
[/equation]
Combining the two equations above, we can represent power as follows:
[equation caption=”Equation 4.3 Equation for power in terms of voltage and resistance”]
$$!P=\frac{V^{2}}{R}$$
where P is power, V is potential energy, and R is resistance
[/equation]
Thus, if you know any two of these four values you can get the other two from the equations above.
Volts, amps, ohms, and watts are convenient units to measure potential energy, current resistance, and power in that they have the following relationship:
1 V across 1 Ω of resistance will generate 1 A of current and result in 1 W of power
The above discussion speaks of power (W), intensity (I), and potential energy (V) in the context of electricity. These words can also be used to describe acoustical power and intensity as well as the air pressure amplitude changes detected by microphones and translated to voltages. Power, intensity, and pressure are valid ways to measure sound as a physical phenomenon. However, decibels are more appropriate to represent the loudness of one sound relative to another, as well see in the next section.