amplitude
Amplitude is a term used in mathematics as well as physics and technology to describe vibrations . It can be used for quantities such as an alternating voltage and its course over time. It is defined as the maximum deflection of a sinusoidal variable from the position of the arithmetic mean . The term can also be applied to waves when the oscillation spreads locally at a constant speed (sine wave).
In DIN 40110-1 a distinction is made between
- Peak value of a periodic alternating voltage and
- Amplitude of a sinusoidal alternating voltage.
For other terms that are not restricted to alternating quantities, but are generally used for periodic processes, e.g. B. for mixed voltage , see under peak value .
In the case of vibrations, the distance between maximum and minimum is referred to as the vibration width or also as the peak-valley value (previously called the peak-peak value).
Mathematical representation
An undamped sinusoidal or harmonic oscillation is caused by
described with the amplitude , angular frequency and zero phase angle . The amplitude is independent of time and therefore constant.
Another possibility of description is the complex representation using Euler's formula (with the symbol for the imaginary unit that is common in electrical engineering :)
- .
This form makes many calculations easier, see Complex AC Calculation . The expression
is the complex amplitude , whose magnitude is equal to the amplitude and whose argument is equal to the zero phase angle .
In certain contexts, the amplitude can also change slowly compared to the associated oscillation, e.g. B. at damping or modulation .
A weakly damped, non-periodic oscillation is caused by the decay coefficient
described. The expression
is the time-varying amplitude function .
For specific influencing of the amplitude, see amplitude modulation .
Examples
The amplitude is illustrated with mechanical examples, especially on the pendulum .
In the ideal case, a spring pendulum (undamped) performs a sinusoidal oscillation. The distance between
- the turning point at which the pendulum has the greatest deflection, and
- the point of rest from which the pendulum cannot oscillate without energy input,
is the amplitude.
A plane physical pendulum swings in a sinusoidal manner neither in the angle nor in the horizontal deflection, even with undamped movement. The horizontal distance between the turning point and the point of rest is a peak value . Only with a small deflection, when the peak value is much smaller than the pendulum length, i.e. if the small-angle approximation can be used, the oscillation becomes sinusoidal and the peak value becomes the amplitude.
Demarcation
The limit values of the deviations from the respective mean value in other curves in graphical representations are also referred to as amplitude in the broader sense. Sometimes the amplitude is also assigned a different meaning, such as the difference between the minimum and the maximum . Here, the technical term has been adopted in the technical terminology of other specialist sciences that do not use it according to the standard defined above , so that the special meaning is occasionally uncertain, for example in pulmonology in spirometry , in seismology in the seismogram or in the Meteorology and climate geography in the climate diagram .
literature
- Ilja N. Bronstein, Konstantin A. Semendjaev, Gerhard Musiol, Heiner Mühlig: Taschenbuch der Mathematik. 5th, revised and enlarged edition, unaltered reprint. Harri Deutsch, Thun et al. 2001, ISBN 3-8171-2005-2 .
- Christian Gerthsen: Physics , Springer-Verlag
See also
Web links
Individual evidence
- ↑ IEC 60050, see DKE German Commission for Electrical, Electronic and Information Technologies in DIN and VDE: Internationales Electrotechnical Dictionary - IEV
- ↑ DIN 1311-1: 2000: Vibrations and systems capable of vibrating - Part 1: Basic terms, classification .
- ↑ ^{a } ^{b } ^{c} DIN 5483-1: 1983: Time-dependent quantities; Names of time dependency .
- ↑ ^{a } ^{b } ^{c} DIN 40110-1: 1994: AC quantities; Two-wire circuits .
- ↑ DIN 1311-4: 1974: Schwingungslehre - Schwingende Kontinua, waves .
- ↑ DIN 1302 : 1999: General mathematical symbols and terms .
- ↑ wetter.net