Sine wave

A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation. In engineering, signal processing, and mathematics, Fourier analysis decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.

When any two sine waves of the same frequency (but arbitrary phase) are linearly combined, the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the sine and cosine components, respectively.

Audio example

A sine wave represents a single frequency with no harmonics and is considered an acoustically pure tone. Adding sine waves of different frequencies results in a different waveform. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, which is the reason why the same musical pitch played on different instruments sounds different.

Sinusoid form

Sine waves of arbitrary phase and amplitude are called sinusoids and have the general form:

y

(

t

)

=

A

sin

⁡

(

ω

t

+

φ

)

=

A

sin

⁡

(

2

π

f

t

+

φ

)

{\displaystyle y(t)=A\sin(\omega t+\varphi )=A\sin(2\pi ft+\varphi )}

where:

A

{\displaystyle A}

, amplitude, the peak deviation of the function from zero.