# http://colinraffel.com/wiki/

### Site Tools

useful_approximations

# Useful approximations

This is an attempt to keep track of the various numbers and approximations that are good to have in your hip-pocket when studying audio and music.

## Physics

• Sound travels roughly 1 foot every millisecond.
• Typical t60 for a small, house-sized room is .5 seconds, for a larger room (eg, classroom) it's about 1 second.
• A 20 Hz signal has a period of 50 milliseconds ( .05 seconds), a 20,000 Hz signal has a period of 50 microseconds ( .00005 seconds)

## Perception

• Humans can usually hear from about 20 Hz to 20,000 Hz (20 kHz)
• Perception of “loudness” for different frequencies is (very) roughly flat from about 100 Hz to 10 kHz, for most decibel levels. Pitches sound much less loud outside of this range.
• A quarter of a decibel change in intensity is the threshold of perception.
• 30 dB SPL is basically unattainably quiet, 60 dB SPL is a normal conversion, 90 dB is around where hearing damage begins
• An increase of 9 dB corresponds to roughly a doubling in perceived loudness.

## Digital Audio

• About 6 dB of Signal to Noise Ratio is gained per bit when quantizing continuous values.
• In order to avoid aliasing, the sampling frequency must be two times that of the highest frequency present in the signal.
• 44100 Hz = .00002675737 seconds between samples, 48000 Hz = .000020833333 seconds between samples

## Instruments

• Guitar frequency range: 82 Hz to 1,300 Hz (E2 = 82.34, 4 octave range)
• Electric guitar pickup output varies from .1 to 1 V RMS, depending on pickup strength
• Piano frequency range: 28 Hz to 4200 Hz (A0 = 27.5, 7+ octave range)