## Thursday, 14 August 2008

### Harmonic Frequencies Of Sine wave

In trigonometric form, a sinewave can be written as

• A sin (x + K) or

• A sin (2 p f t + K)

In another words, the waveform can be mathematically expressed in terms of angle (x) or frequency (f).

Here, the "f" is termed the Fundamental frequency, being the main frequency component of the sinewave.

However, some complicated waves do exist. An example is our speech.

This complicated wave consists of not only the fundamental sine and cosine waves but also their harmonic frequencies, or simply, harmonics.

Harmonic frequencies, what is it?

It is the integer multiples of the fundamental frequency.

If a wave is given as sin 2 p f t,

then the fundamental frequency is f, with

the second harmonic frequency as 2f,

the third harmonic frequency as 3f, and

the "nth" harmonic frequency as nf.

Remarks:

These harmonics are useful information in the analysis and design of audio or musical equipment as they reflect the ability of the equipment (or system) to produce signal close to theoretical target.

An example of an audio equipment that deals with harmonics is the Musical Equaliser that boost and damp down relevant frequencies to obtain the desired acoustic fidelity.

Another application for harmonics study is the analysis of cable bandwidth. It defines the range of operating frequencies that can pass through the cable. The wider the bandwidth, the better is the transmitted signal.

Using maths is one way to figure and explain the "stories" behind all the happenings in real life issues and applications.

Love math !

:)