Write the function in terms of x.

Question

Sounds are how we perceive pressure waves in the air. The note F-sharp, more than an octave below the note 'middle C', is a sound wave with an ordinary frequency* f=105.6 Hertz or cycles/sec.

Model this note with the sine function, assuming that the amplitude is 1 and the phase shift is 0. Write the function in terms of x.

g(x) = ?

*This frequency is based on the just-intonation scale. The frequency based on the equal tempered scale would be f=103.8262

Answer 1

The sound wave as a sine function (of pressure or expansion) can be written as Asin(2πft + δ)

A is amplitude, δ is phase shift, and f is the frequency. The constant in front of the t term is 2πf = ω, the angular frequency.