Frequency

Frequency:

Frequency in oscillation is the number of cycles per second, and in wave motion, it is the number of waves that pass through a given point per second. These cycles per second are called Hertz (Hz) in honor of nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894), who greatly advanced understanding of electromagnetic wave behavior during his short career.

Denotation:

In physics and technology disciplines, such as optics, acoustics, and radio, frequency is generally denoted by a Latin letter f or by a Greek letter ν (nu).

SI Unit:

In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. 1 Hz means that a happening repeats one time per second. A previous name for this unit was cycles per second.

A customary unit of measure utilized with rotating mechanical devices is revolutions per minute, abbreviated RPM. 60 RPM equals one hertz.

Formula:

The time span, usually denoted by T, is the extent of time taken by one cycle, and is the reciprocal of the frequency f:

T=1/f

The SI unit for period is the second.

Lissajous Figures

Lissajous Figures:

A Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissaajous (French) in 1857.

Generation:

Prior to modern computer graphics, Lissajous curves were typically generated using an oscilloscope (as illustrated). Two phase-shifted sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure. Lissajous curves can also be traced mechanically by means of a harmonograph.

Uses of Lissajous figures:

Lissajous Figures displays the motion of a superposition of two perpendicular harmonic oscillators. The simulation shows the result of the superposition. The amplitude and frequency of the oscillators can be changed. Here are some examples of Lissajous figures.