Definition of frequency

The number of times to complete vibration per unit time is a quantity describing the frequency of reciprocating motion of vibrating objects, which is usually represented by symbol F or V, and the unit is-1. In order to commemorate the contribution of German physicist Hertz, people call the unit of frequency Hertz for short. Every object has a frequency independent of amplitude, which is determined by the nature of the object itself and is called the natural frequency. The concept of frequency is not only used in mechanics and acoustics, but also in electromagnetism and radio technology. The number of times that alternating current completes periodic changes in unit time is called the frequency of current.

[Edit this paragraph] Physical:

The number of times a substance completes a periodic change in 1 s is called frequency, which is often expressed by F.

In physics, the unit of frequency is hertz (Hz), and it is also commonly used as kilohertz (kHz) or megahertz (MHz) or GHz. 1kHz= 1000Hz， 1 MHz = 100000hz 1 GHz = 1000 MHz。 The frequency f is the reciprocal of the period t, that is, f = 1/t, and the wave velocity = wavelength * frequency. The electricity used in China is sinusoidal alternating current with a frequency of 50Hz, which means that it makes 50 periodic changes in one second.

In addition, the sound we hear is also a wave with a certain frequency. The frequency range of human hearing is about 20-20-20000HZ. Beyond this range, our ears will not notice it.

In astronomical tide science, it is inconvenient to express the frequency by hertz because of the long activity period of various celestial bodies. The common frequency unit is cph, that is, it circulates every hour. For example, the period of the most common M2 tidal component is about 12.42 hours, and its frequency is usually expressed as 0.0805 1cph.

[Edit this paragraph] Frequency in mathematics:

Under the same conditions, n experiments were carried out. In these n experiments, the frequency nA of event A is called the frequency of event A. The ratio of nA/n is called the frequency of event A, and it is denoted as fn(A).

1. When the number of repeated experiments n increases gradually, the frequency fn(A) shows stability and gradually stabilizes at a certain constant, which is the probability of event A. This "frequency stability" is also called statistical regularity.

Frequency is not equal to probability. According to Bernoulli's theorem of large numbers, when n approaches infinity, frequency fn(A) approaches probability P(A) in a certain sense.

English definition: frequency

[Edit this paragraph] Frequency calculation in mathematics:

The relative frequency m/n of random events appearing m times in n tests. In general physical science, frequency refers to the number of vibrations per second, which can be random or deterministic.

Under certain conditions, observing or testing the studied object is called a test every time the condition group is realized. The result is called an event. In experiments, events that may or may not occur are called random events.

The probability p(A) of random event A is a measure of the probability of this event. Its value is between 0 and 1. Under certain conditions, if event A is impossible, then p (a) = 0; If event A must occur, then p (a) = 1. With the increase of test times n, the probability of frequency approaching is greater, that is:

Where δ is an arbitrary decimal value.

Hydrological phenomenon is a complex natural phenomenon, and its occurrence probability cannot be known, which can only be inferred by counting the occurrence frequency in the measured hydrological data. Due to the limitation of data, there will always be some errors.

The random variable X, which describes hydrological stochastic phenomena, generally belongs to continuous type. Therefore, the probability that x equals any number x is p {x = x}. Cumulative percentage curve FX (x) ~ x is used to describe the statistical characteristics of hydrological variables in hydrological calculation. If the probability of annual flood peak discharge at Yichang Station of the Yangtze River is greater than or equal to 80000m3/s, p{X≥80000}=FX(80000).

In hydrological calculation, the frequency density function FX(x) of hydrological variables is generally estimated by statistical analysis based on measured data, and then the cumulative percentage function fX(x) of hydrological variables can be obtained by integrating fX(x) (see figure):

In hydrological calculation, it is customary to call cumulative percentage curve FX(x) as frequency curve and FX (x) ~ x curve as frequency density distribution curve.

[Edit this paragraph] Doppler effect

Although sound has only a constant frequency, it sometimes changes for the listener. When there is relative motion between the wave source and the listener, the phenomenon that the listener feels the frequency change is called Doppler phenomenon.