Frequency The number of cycles

Frequency—The number of cycles of an oscillating motion which occur per second. For example, if the period for one cycle is 0.5 second, then the frequency is (1 cycle)/(0.5 second) = 2 cycles per second = 2 Hertz. 

Frequency - The number of cycles through which an alternating current passes per second in the U.S. the standard for electricity generation is 60 cycles per second (60 Hertz). 

French mold See mold, French, frequency The number of cycles that are completed or required in a unit of time. See attenuation period, frequency bandwidth The range of frequencies within which performance of a component is accurate, usually extending from zero frequency to some cutoff frequency. 

Variable nozzles produce a series of jets of gas entering the rotor, and these impulses add up to form a frequency equal to the blade-passing frequency the number of revolutions per second multiplied by the number of nozzle vanes, which is of the order of thousands of cycles per second. Frequently the rotor will resonate at this frequency, and if it does, it will be fatigued and crack and break up thus these frequencies must be avoided, and the manufac turer should be asked to supply information to the customer on this subject. 

The reciprocal of r gives the number of cycles per unit time, which is the frequency v of the rotation. The velocity u, may then be expressed as... 

Hz = Hertz, unit of frequency - the number of times a wave oscillates per unit time - measured in cycles per second. 

Fig. 5. Pulse sequence for MR detection of vibration using a radiofrequency field gradient. A binomial 1331 radiofrequency pulse (pulse length D, interpulse delay r) is applied in-phase with the mechanical wave. Thus the vibration period 7V is equal to 4(D + r). The number of cycles can be increased to ensure a better frequency selectivity. The constant RF field gradient generated by a dedicated RF coil allows space encoding without using conventional static field gradients (from Ref. 16 with permission from Elsevier).

The tendency of premixed flames to detach from the flame holder to stabilize further downstream has also been reported close to the flammability limit in a two-dimensional sudden expansion flow [27]. The change in flame position in the present annular flow arrangement was a consequence of flow oscillations associated with rough combustion, and the flame can be particularly susceptible to detachment and possible extinction, especially at values of equivalence ratio close to the lean flammability limit. Measurements of extinction in opposed jet flames subject to pressure oscillations [28] show that a number of cycles of local flame extinction and relight were required before the flame finally blew off. The number of cycles over which the extinction process occurred depended on the frequency and amplitude of the oscillated input and the equivalence ratios in the opposed jets. Thus the onset of large amplitudes of oscillations in the lean combustor is not likely to lead to instantaneous blow-off, and the availability of a control mechanism to respond to the naturally occurring oscillations at their onset can slow down the progress towards total extinction and restore a stable flame. 

Frequency The number of times a periodic wavelength cycle occurs in 1 s the unit of measurement is hertz (Hz). 

Bills (7) has applied an adaptation of this law to solid propellants and propellant-liner bonds for discrete, constantly imposed stress levels considering U to be the time at the ith stress level and tfi the mean time to failure at the ith stress level. A probability distribution function P was included to account for the statistical distribution of failures. For cyclic stress tests the time is the number of cycles divided by the frequency, and the ith loading is the amplitude. The empirical relationship... 

Ultrasonic waves are a mechanical disturbance which passes thru the medium by the progressive displacement of particles. The particles do not travel in the direction of the source but vibrate about their mean fixed position. The amplitude of the wave is the distance from peak to peak and therefore is the maximum displacement of a particle in the medium. The period (T) is the time required to complete one cycle and the frequency (f) refers to the number of cycles per unit time. The unit of frequency is the Hertz (Hz, one cycle per second) and it is the reciprocal of the period. The rate at which sound travels thru the medium is the velocity (c, meters per second). The wavelength (X, meters), is the distance between adjacent cycles. Therefore, the relation,between wavelength, velocity and frequency is given by... 

The range of frequency specified is between 1 and 5 Hz and the standard only covers strain cycles passing through zero, although prestrains could be applied. It is suggested that at least five test pieces should be tested at each strain and that usually it is desirable to test at a number of maximum strains. The strain on ring test pieces is calculated on the internal diameter (see Chapter 8, Section 5.1). The test is continued until complete failure of the test piece occurs and then the number of cycles recorded. 

An electric field pushes on charged particles such as electrons. As a light ray passes an electron, its electric field pushes the electron first in one direction, then in the opposite direction, over and over again (Fig. 1.1). That is, the field oscillates in both direction and strength. The number of cycles (complete reversals of direction away from and back to the initial strength and direction) per second is called the frequency, v (the... 

The catalyst turnover number (TON) and the turnover frequency (TOF) are two important quantities used for comparing catalyst efficiency. Their definitions, however, vary slightly among the three catalysis fields. In homogeneous catalysis, the TON is the number of cycles that a catalyst can run through before it deactivates, i.e., the number of A molecules that one molecule of catalyst can convert (or turn over ) into B molecules. The TOF is simply TON/time, i.e., the number of A molecules that one molecule of catalyst can convert into B molecules in one second, minute, or hour. In heterogeneous catalysis, TON and TOF are often defined per active site, or per gram catalyst. This is because one does not know exactly how many... 

Now suppose we move counter-clockwise along the circle at a constant speed, which we will call co. co has units of radians per second, and is also called the angular velocity. The x- and j-coordinates will vary with time as shown in Figure 1.2. Notice that the waveform is the same for the cosine (x-coordinate) and the sine (y-coordinate) except for a shift of one-quarter cycle. The frequency of the sine wave, commonly denoted by the symbol v, is the number of cycles per second. This unit is given the special name of Hertz. Since there are 2n radians in one cycle, co = 27rv. One complete cycle requires a time T = 2jt/o> = 1/v, which we call the period of the sine wave (seconds per cycle). 

If a wave persists only for a time At (or if we can only measure its frequency for a finite time At), the frequency is intrinsically unknown by an amount (1/4 At). For example, suppose we try to measure the frequency of a sound wave by using a microphone and an oscilloscope to count the number of cycles in one second. We could readily distinguish between a sound wave at 1000 Hz and one at 1001 Hertz, because the faster wave will go through one more cycle (in fact, your ear would hear a beat as the notes went in and out of phase with each other). It would be nearly impossible to distinguish between a wave at 1000 Hz and a wave at 1000.001 Hz at the end of one second, they would still be nearly perfectly in phase with each other. 

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