The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:
where:
- A, the amplitude, is the peak deviation of the function from zero.
- f, the ordinary frequency, is the number of oscillations (cycles) that occur each second of time.
- ω = 2πf, the angular frequency, is the rate of change of the function argument in units of radians per second
- φ, the phase, specifies (in radians) where in its cycle the oscillation is at t = 0.
- When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.
The sine wave is important in physics because it retains its waveshape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.
Read more about Sine Wave: General Form, Occurrences, Fourier Series, Traveling and Standing Waves
Famous quotes containing the words sine and/or wave:
“Hamm as stated, and Clov as stated, together as stated, nec tecum nec sine te, in such a place, and in such a world, that’s all I can manage, more than I could.”
—Samuel Beckett (1906–1989)
““Justice” was done, and the President of the Immortals, in Æschylean phrase, had ended his sport with Tess. And the d’Urberville knights and dames slept on in their tombs unknowing. The two speechless gazers bent themselves down to the earth, as if in prayer, and remained thus a long time, absolutely motionless: the flag continued to wave silently. As soon as they had strength they arose, joined hands again, and went on.
The End”
—Thomas Hardy (1840–1928)