Question

An electronic tuning aid is often used by a piano tuner to properly tune a piano. The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz. Write a sine model that gives the Tone, T, as a function of time, t, for this key.

Answer 1

T = sin(6572t)

Explanation:

A pure tone is a sine-wave and sine-waves are defined by ω (omega) and t (time)

For a sine model:

Amplitude of wave form = sin(ωt)

A sine model that gives the Tone, T, as a function of time, t, for this key:

T = sin(ωt)

Sin is a mathematical operator in trigonometry

ω = 2πf

π = 3.14

The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz.

f = 1046.5 hertz

ω = 2×3.14×1046.5

ω = 6572.02

T = sin(6572t)