Mersenne’s laws Acoustics Noise-to-signal ratio Commentary

Pythagoras, Vincenzo Galilei, Marin Mersenne acoustics

Mersenne’s laws

• Pythagoras understood the first law of vibrating strings—
• pitch is inversely proportional to the length of the string.
• Pythagoras also knew that the series of harmonic overtones
• were related to the series of whole-number multiples.
• Moving right along, it turned out that musicians
• knew how to tune their lutes without Pythagoras.
• Galileo’s father, Vincenzo, a musician, certainly realized
• that pitch also depends on how tight and how thick the string is.
• He was the first to describe a natural phenomenon
• using a non-linear mathematical equation.
• Specifically, he added the second law of vibrating strings—
• pitch is proportional to the square root of the tension.
• Finally, Marin Mersenne added the third law—
• pitch is inversely proportional to the square root of the heaviness of the string.

Acoustics

• Vitruvius wrote a treatise
• on the acoustics of theaters,
• recognizing that sound is a three-dimensional
• equivalent of waves on a water’s surface.
• Vincenzo Galilei, in addition
• to explaining the second law,
• noted that pitch depends on the properties
• of the space the string vibrates in.
• Galileo Galilei said, “Waves are produced by the vibrations
• of a sonorous body, which spread through the air,
• bringing to the tympanum of the ear a stimulus
• which the mind interprets as sound.”
• Isaac Newton’s inverse-square law
• applies to sound as well as gravity.
• In Principia Mathematica, Newton also
• derived the relationship for wave velocity in solids.

Noise-to-signal ratio

• I can hear you
• in this restaurant
• but I don’t know what
• you’re saying.
• A great roar
• arises from little mouths
• talking louder
• to be heard over the roar.
• We vibrate
• our vocal chords
• which vibrate air
• in each other’s direction
• but our lips
• are a better
• indicator
• of our accord.