Sine is a periodic function.
Its graph is called a sinusoidal curve
and by specifying its frequency (period), mean level, amplitude, and phase shift,
can be used to model periodic phenomena
like daily tides, annual temperature, circadian rhythms, etc.
One of the earliest uses was for modelling pendulums
to build devices that accurately reflected the procession of time: clocks.
The standard unit of measuring frequency is Hertz (Hz),
where 1 Hz represents one cycle per second.
An accurate pendulum clock “ticks” at a rate of 1 Hz.
Sound (acoustic waves) consist of vibrations passing through matter that causes oscillating wave of pressure. The pitch of a sound is the frequency of its pressure wave. The volume or “loudness” of sound comes from the intensity of pressure wave, related to its amplitude. Human ears can perceive some of these pressure waves, particularly the ones with frequencies between 20 Hz and 20 kHz (20,000 Hz). For reference the “censor” bleep tone is 1000 Hz. Sound travels through dry temperate air at about or 750 mph, which makes wavelengths of frequencies humans can hear between 56ft and ⅔in long.
Light (electromagnetic radiation) is radiant energy manifesting as a wave. Human eyes can perceive some of these electromagnetic waves, particularly the ones we call visible light with frequencies in the range 420–750 THz (420,000,000,000,000–750,000,000,000,000 Hz). For reference the color “orange” is about 600 THz. The speed of light in a vacuum (space) is about 700,000,000 mph, making the wavelengths of visible light about 2 hundred-thousandths of a inch. The frequencies humans can’t perceive include microwaves, radio waves, and X-rays. Concerning radio waves, FM radio broadcasts on carrier waves in the 88–108 MHz (88,000,000–108,000,000 Hz) frequency range, while AM radio broadcasts on carrier waves in the 530–1700 kHz (530,000–1,700,000 Hz) frequency range.
Fourier Analysis: A function modelling a wave over time can be decomposed into a sum of sinusoidal waves of different frequencies.