# Andy's Hearing Sandbox

1. Question:
(From this site:)

Loudness of a sound is proportional to the square of the amplitude of the vibration producing the sound. Explain.

Solution:
The loudness of sound depends on the amplitude of vibration of the vibrating object. Greater the amplitude of vibration, louder the sound will be.

When a Sitar string is plucked lightly, then it vibrates with a small amplitude and produces a faint sound or feeble sound. When a sitar string is plucked hard, then it vibrates with a large amplitude and produces a very loud sound.

The loudness of sound is directly proportional to the square of the amplitude of vibration.

If the amplitude of vibration is doubled, then the loudness will become 4 times.

If the amplitude of vibration is halved, then the loudness will become one-fourth.

The loudness of sound is expressed in the units called the Decibel. The symbol of the decibel is Db.

At a loudness of above 80 Db, the sound become physically painful. And at about 140 Db level, the sound hurts too much.

2. Mathematica ${\displaystyle f(\theta )}$
3. Decibel -- a tenth of a Bel, of course!:)

The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 101⁄20 (approximately 1.12).

....

Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm in base 10.[5] That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.

4. Joe's suggestions:
5. I did a search for Mathematica and hearing tests, and found a few interesting articles:

6. Went looking for Mathematica synthesizers, and
7. Encylopedia Britanica has a good article on sound

8. I’d said I’d look into analysis for python and R: here are some early looks

9. Soundmagic Spectral:
• "SoundMagic Spectral is a freeware suite of 23 Audio Unit plug-ins that implement real-time spectral processing of sound. This set of effects give you unprecedented control and creativity in the processing of audio, whether from static audio files or live audio streams."
• Only for the Mac at this time...:(