# What is the mathematical formula to turn a particular sound frequency to a related color?

###### February 22, 2008 4:05PM

There are many possible formulas. The simplest would be to map the hearing range directly to the visible. The speed of sound in air is about 300 meters per second and the speed of light is about 3e8 meters per second. We can hear frequencies of 20 to 20,000 Hz, and that corresponds to wavelengths of 15 down to .015 meters. We can see wavelengths from 700 nanometers down to 400 nanometers. So a straight formula would be

light wave length = 20e-9 * (sound wave length) + 399.7e-9 (in meters)

sound wave length = 300 / (sound frequency in Hz) (in meters)

Another way would be to compress the sound into octaves and let that be a linear

mapping. This would be like assigning the keys on a piano to specific colors. A

formula for that might be

light wave length = 100 * (Log (sound wave length)) + 582.4 (in nanometers)

(and I used the same formula for sound wave length above).