# 9.2 Dynamic range

The quietest sound we can hear corresponds to a pressure wave with an amplitude of about 10 μPa, which is a very small pressure amplitude indeed. It is about 0.000 000 01 per cent of nominal atmospheric pressure, and the resultant displacement of the eardrum is less than a tenth of the diameter of a hydrogen molecule.

At the upper end of the scale, a sound that is distressingly loud might typically correspond to a pressure wave with an amplitude of 0.01 per cent of nominal atmospheric pressure or more. (Atmospheric pressure itself varies from day to day, which is why I refer to a ‘nominal’ value of atmospheric pressure.) We call a range of sound amplitudes such as this a dynamic range. From the figures given here, it is clear that the loudest sounds we encounter can have an amplitude more than a million times greater than the quietest.

The size of the human dynamic range comes as a surprise to many people. Loud sounds, subjectively, do not seem to exceed quiet ones by a factor of a million. The reason for this relates to the non-proportional relationship between amplitude and loudness that we met in Section 6. With quiet sounds, we readily notice a small increase in the amplitude. For instance, two bicycle bells ringing sound distinctly louder than one. But if the same increase is made to a louder sound (for instance, 11 bicycle bells instead of 10), the change is not so noticeable. Research into the perception of sound indicates that instead of hearing equal increments of amplitude as equal increments of loudness, we hear equal multiples of amplitude as equal increments. For instance, successive doublings of the amplitude of a sound are generally perceived as equal increments of loudness. This is somewhat akin to the way we hear successive doublings of frequency as equal increments of pitch.

## Activity 30 (Listening, Exploratory)

Listen to the audio below.

- (a) In the first part, you hear a quiet sine wave that grows in amplitude by successive doublings and then decreases by successive halvings. Does the loudness seem to change by the same amount each time?

- (b) In the second part, you hear the sine wave grow in amplitude by equal increments and then decrease by equal decrements. Does the loudness seem to change by the same amount each time?

Click 'Play' to listen to Audio Clip

This browser does not support audio playback.

### Discussion

I expect you answered ‘yes’ to (a) and ‘no’ to (b). (Depending on your audio equipment, you may not have heard all the changes in (b). There are as many steps in (b) as in (a).)

OpenLearn - Sound for music technology: An introduction
Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.