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. The sine wave occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields.
The sine wave is important in physics because it retains its wave shape 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.
In 1822, French mathematician Joseph Fourier discovered that any wave could be modeled as a combination of different types of sine waves. This applies to unusual waves like square waves and highly irregular waves like human speech.
The discipline of reducing a complex wave to a combination of sine waves is called Fourier analysis, and is fundamental to many of the sciences, especially those involving sound and signals. Fourier analysis is central to signal processing and the analysis of time series, where seemingly random sets of data points are studied to elucidate a statistical trend.
Fourier analysis is also used in probability theory, where it is used to prove the central limit theorem, which helps to explain why bell curves, or normal distributions, are ubiquitous in nature.
The human ear can recognize single sine waves as sounding clear because sine waves represent a single frequency with no harmonics. Some sounds that replicate a pure sine wave are whistling, a crystal glass made to vibrate by running a wet finger around its rim and the sound made by a tuning fork.
The power that is generated and supplied by your local utility is a sine wave. This is because it is generated by rotating AC machinery and since waves are a natural product of rotating AC machinery.
However, just because sine wave AC is provided by your utility at your outlet doesn’t make it the only, nor the best waveform to use to backup your computer. There are other factors to consider. In fact, for computer power supplies, most engineers would tell you it would be better if smooth DC came out of the wall outlet instead of AC sine waves.
Sine waves are great for power companies to make and transmit power over great distances, however, DC runs modern microcomputers. Interestingly enough, it turns out that square waves, and quasi-sine wave pulse width modulated stepped rectangular waveforms, make better sources for rectification into smoother more ripple free DC voltage than do sine waves.
The reason for this is that these “flat-topped” waveforms have a higher average output voltage value and the output voltage is at peak value longer than for “round-topped” sine waves. Charging of a DC power supply occurs at the peak of the waveform, since flat-topped waveforms are at the peak longer they keep the DC supply input fully charged longer and thus the DC output is smoother. This reduces ripple and improves the system power factor.
This can be easily demonstrated by attaching an oscilloscope on the output of a DC smoother with the flat-topped waveforms than for round-topped sine waves.