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If we want to provide the user with a вЂњfully linear volume control sensation,вЂќ we would need to know how вЂloudвЂ™ their audio equipment plays at its loudest setting. To determine the correct value for b, we need more information. The major problem is that even though the hearing threshold is roughly the same across different persons, the loudness produced by any audio system for a given signal amplitude depends on a multitude of parameters. Moreover, in any normal environment with background noise, sounds with a loudness below the noise level will already be inaudible. This is not a problem because the logarithmic response curve of our ears also hits zero below a certain non-zero input loudness, the hearing threshold. As I said above, our exponential volume control will inevitably still have a non-zero amplitude at the zero slider position. If you are still thinking linearly you might be tempted to pick (0,0) as the second point, which it is not. It is not perfect, but a billion times better than a linear slider! If you cannot afford implementing a true exponential curve, use this simple formula for your volume slider. Table 1 shows similar approximations for other dynamic ranges. In other words: amplitude multiplication factor = x 4. This approximation is the 4th power of the volume slider's position x scaled to the interval.

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If for some reason you don't want to implement a full exponential function, you can instead rely on a good all-round and computationally cheap approximation that fits the typical 60 dB range of low-to-medium powered consumer audio systems.

2 dB is pretty much ideal as a step size. Volume changes below 1 dB are not noticeable and changes above 3 dB are too coarse.

If you want to offer a way of changing volume by discrete increments, like pushing buttons or turning a mouse scroll wheel, make sure the increments are somewhere between 1 dB and 3 dB.

Add a linear roll-off near zero if you want to ensure perfect silence at volume setting 0. Again, you should probably use the parameters for 60 dB range.

x) for various figures of loudness ranges x is the slider's relative position in the interval and y is the actual scale factor for the sound waveform.

Table 1 shows some practical values of parameters a and b in the formula y = a.

A good assumption for consumer equipment is that the user will have a usable range of 60 dB.

Unless you are working on a high-end product with known specifications, you will need to make some guesses and approximations.

The problem with this is that one can in general only make vague assumptions about what equipment the user will be using.

x), with its lowest setting corresponding to вЂsilenceвЂ™ (typically 30 dB(A) for consumer products) and its highest setting the maximum loudness the user's audio equipment produces.

The ideal volume slider follows an exponential curve y = a.

A percentage is only acceptable if it maps to dB values, e.g.

A volume control should not be based on percentages, because this implies linearity.

In practice, a вЂsilentвЂ™ room will be at в“0 dB(A). To measure absolute loudness as perceived by humans, the dB(A) scale is often used, with 0 dB(A) the loudness of the most silent perceivable sound. Multiplying amplitude by a certain factor means adding a certain amount of dB. Positive dB values mean amplification, negative values attenuation. For a relative amplitude level x, the dB value equals 20*log 10( x). That is why all audio equipment worth its name uses the dB scale to indicate volume and gain settings. Linear volume sliders are a nuisance because human perception of loudness is not linear at all, it is logarithmic. For those with little time, here is the essence of this text compressed into a few sentences: