Occurrences Sine wave

illustrating cosine wave s fundamental relationship circle.

this wave pattern occurs in nature, including wind waves, sound waves, , light waves.

a cosine wave said sinusoidal , because



cos
⁡
(
x
)
=
sin
⁡
(
x
+
π

/

2
)
,


{\displaystyle \cos(x)=\sin(x+\pi /2),}

sine wave phase-shift of π/2 radians. because of head start , said cosine function leads sine function or sine lags cosine.

the human ear can recognize single sine waves sounding clear because sine waves representations of single frequency no harmonics.

to human ear, sound made of more 1 sine wave have perceptible harmonics; addition of different sine waves results in different waveform , changes timbre of sound. presence of higher harmonics in addition fundamental causes variation in timbre, reason why same musical note (the same frequency) played on different instruments sounds different. on other hand, if sound contains aperiodic waves along sine waves (which periodic), sound perceived noisy noise characterized being aperiodic or having non-repetitive pattern.