The Relationship Of Voltage, Loudness, Power and Decibels


Loudness, to a great degree, is subjective. What is loud to one person is not to another. Thus we need a measure that allows us to quantify what we hear.
The unit of measure most common is the decibel (dB). Most audiophiles are familiar with the term, but just what does it actually mean?

Without getting too technical, the dB is a unit of measure for sound intensity or level. It is a logarithmic scale developed to express wide-ranging quantities on a simple scale. Because it is logarithmic, it can be a little bit confusing.
As an example, a doubling of the volume is not equal to twice the number of dB. The chart below will help you to better understand the dB and how it relates to what you hear, and what is happening throughout your system as volume levels change. But first, we need to look at the other end of the equation.

Power, in this discussion, refers to watts. Power defined is the rate at which energy is converted or dissipated, as in the case of an amplifier driving a loudspeaker. It is important in our discussion in defining the general relationship.

dB Change Voltage Power Loudness
3 1.4X 2X 1.23X
6 2.0 4.0 1.52
10 3.16 10 2
20 10 100 4
40 100 10,000 16

Looking at the chart, and starting at the left, we can see that an increase of 3dB results in a voltage increase 1.4 times the original, a doubling of power, and yields only a subjective increase in loudness only 1.23 times the original.

To get a doubling of loudness, it is important to note that an increase of 10dB is necessary. And to reproduce that volume through our loudspeakers, note that we require ten times more power from the amplifier!

The implications of this comparison in a typical hi-fi system are significant.
Let us assume that you are listening to your stereo at a comfortable volume of 8OdB. We will further assume that this level requires 25 peak watts from your amplifier. To just barely increase the volume, we might increase loudness by 3dB.
As we can see from the chart, this will require a doubling of power from the amplifier, which will now be churning out 50 peak watts to produce a loudness of 83dB.
If we want to double the apparent volume from our original level we will need to create 9OdB of sound pressure, requiring 250 peak watts.

Many individuals I have spoken with are concerned with having "too much" power. The perception is that an amplifier with an output greater than that recommended by the speaker manufacturer would be likely to damage the speaker.
This is not necessarily so. Interestingly, an underpowered amplifier is more likely to cause speaker damage!

When an amplifier is over-driven, it "clips" the wave-form. What was a clean sine wave becomes a distorted, almost square, wave.
A square wave is extremely difficult for a speaker to reproduce, as it requires virtually instantaneous starting and stopping of the diaphragm. At sufficient power levels, the tweeter will simply die trying to reproduce this wave-form.
A given tweeter rated to handle 50 watts of clean undistorted sine-wave power, will be capable of handling only a fraction of that amount in square-wave input.

As you can see, clean, undistorted power is the key. A 25-watt amplifier, constantly driven to clipping, is more dangerous than a 250-watt amplifier that is never taxed.
I am not saying that speakers can handle endless input, they cannot. However, extra power does not mean that speaker damage is bound to occur.

If common sense is used, any size amplifier can be employed.

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