The frequency of oscillations, number of 1 seconds. Designated. If T is periodotypes of oscillations, then \u003d 1 / t; It is measured in hertz (Hz). Theugal frequency barbecues \u003d 2 \u003d 2 / T rad / s.

The period of oscillations, the smallest period of time through which the fluctuations of the system are in charge of the same condition in which it was at the initial moment, selected arbitrarily. Period - Elevance, reverse frequency oscillations. The "period" is applicable, for example, in the case of harmonic oscillations, however, it is often used for poorly decaying oscillations.

Circular or cyclic frequencyΩ

When changing the cosine argument, or the sinus on 2π these functions are returned to the previous value. We will find the time interval T, during which the phase of the harmonic function varies by 2π.

Ω (T + T) + α \u003d ωt + α + 2π, or ωt \u003d 2π.

Time T one complete oscillation is called a period of oscillation. The frequency ν is called the quantity, reverse period

Frequency measurement unit - Hertz (Hz), 1 Hz \u003d 1 s -1.

Circular, or cyclic frequencies ω 2π times the frequency of oscillations ν. Circular frequency is the rate of phase change over time. Really:

.

Amplitude (from Latin Amplitudo - value), the greatest deviation from the equilibrium value of the value, fluctuating according to a certain, including harmonic, law; Watch solarmonic oscillations.

Phase oscillations The argument of the functionCOS (ωt + φ) describing the harmonic oscillatory process (ω - the circular frequency, T - time, φ is the initial phase of oscillations, i.e. the phase of oscillations of the initial moment of timet \u003d 0)

Displacement, speed, acceleration of the oscillating particle system.

Energy of harmonic oscillations.

Harmonic oscillations

An important particular case of periodic oscillations are harmonic oscillations, i.e. such changes in the physical quantity that go under the law

where. From the course of mathematics it is known that the function of the form (1) changes in the range from A to -A, and that the smallest positive period of it. Therefore, the harmonic oscillation of the form (1) occurs with the amplitude A and the period.

You should not confuse the cyclic frequency and frequency of oscillations. There is a simple connection between them. Since, but, then.

The value is called oscillation phase. At t \u003d 0, the phase is equal to, because the initial phase.

Note that at the same T:

where - the initial phase. Accordingly, the initial phase for the same oscillation is the value defined with the target before. Therefore, from a plurality of possible values \u200b\u200bof the initial phase, the value of the initial phase is the smallest in the module or the smallest positive one. But this is not necessary. For example, oscillation is given then it is convenient to write in the form and to work further with the last view of this oscillation record.

It can be shown that fluctuations of the form:

where any sign will be to be, with the help of simple trigonometric transformations, it is always reduced to the form (1), and, ane is equal to, generally speaking. Thus, the oscillations of the form (2) are harmonic with the amplitude of the cyclic frequency. Do not lead to general evidence, illustrate it on a specific example.

Let it take to show that the oscillation

it will be harmonious and find amplitude, cyclic frequency, periods initial phase. Really,

-

We see that the oscillation of the value S was able to record in the form (1). Wherein ,.

Try yourself to make sure that

.

Naturally, the recording of harmonic oscillations in the form (2) is no worse than the recording in the form (1), and switch to a specific task from recording in this form to record in another form is usually no need. You only need to be able to immediately find the amplitude, cyclic frequency and period, having in front of any form of recording of harmonic oscillation.

Sometimes it is useful to know the nature of the change in the first and second time derivatives from the size of S, which makes harmonic fluctuations (fluctuates for harmonious law). If a , then time differentiation T gives ,. It can be seen that S "and S" "fluctuate also by harmonious law with the same cyclic frequency as the value S, and amplitude, respectively. We give an example.

Let the coordinate of the body, performing harmonic oscillations along the X axis, varies according to the law, where x in centimeters, time T in seconds. It is required to record the law of changing the speed and acceleration of the body and find their maximum values. To answer the assigned question, we note that the first time derivative from the value of x is the projection of the body velocity on the x axis, and the second derivative X is the projection of the acceleration on the x axis: ,. Differentizing the expression for x in time, we get ,. Maximum values \u200b\u200bof speed and acceleration: .

Oscillations - repeated in one degree in time the process of changing the state states near the point of equilibrium.

Harmonic oscillation - oscillations, in which the physical (or any other) varies vary over time according to the sinusoidal or cosine law. The kinematic equation of harmonic oscillations has the form

where X is the displacement (deviation) of the oscillating point from the equilibrium position at the time of T; A - amplitude of oscillations, this is a value that determines the maximum deviation of the oscillating point from the equilibrium position; ω is a cyclic frequency, the value indicating the number of complete oscillations occurring within 2π seconds is the total phase of oscillations, the 0- initial phase of oscillations.

The amplitude is the maximum displacement value or variable changes from the average value with a oscillatory or wave motion.

The amplitude and the initial phase of oscillations are determined by the initial conditions of movement, i.e. The position and velocity of the material point at the time T \u003d 0.

Generalized Harmonic Differential Vibration

the amplitude of sound waves and audio signals usually refers to the amplitude of air pressure in the wave, but is sometimes described as an offset amplitude relative to equilibrium (air or speaker's diaphragm)

Custom is a physical value, a characteristic of a periodic process, equal to the number of complete cycles of the process performed per unit of time. The frequency of oscillations in sound waves is determined by the frequency of source oscillations. High frequency fluctuations fucked faster than low-frequency.

The value, the inverse frequency of oscillations is called a period of T.

Period oscillations - the duration of one full oscillation cycle.

In the coordinate system from point 0, we draw the vector A̅, the projection of which on the axis is equal to ACOSφ. If the vector A̅ is uniformly rotate with an angular velocity ω˳ counterclockwise, then φ \u003d ω˳t + φ˳, where φ˳ is the initial value of φ (oscillation phase), then the oscillation amplitude is the module of a uniformly rotating vector A̅, the oscillation phase (φ ) - the angle between the vector A̅ and the axis oh, the initial phase (φ˳) - the initial value of this angle, the angular frequency of oscillations (ω) - the angular velocity of the rotation of the vector A̅ ..

2. Wave Process Characteristics: Wave Front, Ray, Wave Speed, Wave Length. Longitudinal and transverse waves; Examples.

The surface that shakes at the moment has already covered and not yet covered by fluctuations is called the wave front. In all points of such a surface, after leaving the front of the wave, oscillations are installed, the same phase.

Ray is perpendicular to the wave front. Acoustic rays, like light, are straightforward in a homogeneous medium. Reflected and refracted at the interface of the 2nd environments.

The wavelength is the distance between the two points closest to each other, fluctuating in the same phases, usually the wavelength is indicated by the Greek letter. By analogy with the waves arising in water from the abandoned stone, the wavelength is the distance between two adjacent crests of the wave. One of the main characteristics of the oscillations. Measured in units of distance (meters, centimeters, etc.)

• longitian Waves (compression waves, p-waves) - medium particles fluctuate parallel (by) the direction of propagation of the wave (as, for example, in the case of sound propagation);
• transverse waves (shift waves, s-waves) - medium particles oscillate perpendicular the direction of propagation of the wave (electromagnetic waves, waves on the surfaces of the separation of media);

The angular frequency of oscillations (ω) is the angular velocity of the rotation of the vector A̅ (ѵ), the displacement of the oscillating point - the projection of the vector A̅ on the axis oh.

Ѵ \u003d dx / dt \u003d -aω˳sin (ω˳t + φ˳) \u003d - ѵmsin (ω˳t + φ˳), wherevm \u003d aω˳-maximal speed (speed amplitude)

3. Free and forced oscillations. Own frequency of system oscillations. Phenomenon of resonance. Examples .

Free (own) oscillations Call those that are performed without external influences due to the originally obtained energy of energy. The characteristic models of such mechanical oscillations are the material point on the spring (spring pendulum) and the material point on the non-aggressive thread (mathematical pendulum).

In these examples, the oscillations arise either due to the initial energy (the deviation of the material point on the position of the equilibrium and the movement without initial speed), or due to the kinetic (the body is reported in the initial position of the equilibrium), or at the expense and other energy (speed of the body deviated from the equilibrium position).

Consider the spring pendulum. In the equilibrium position of the elastic force F1

balans the gravity of MG. If you delay the spring at the distance x, a large elastic strength will act on the material point. Change the value of the elastic force (F), according to the law of the throat, is proportional to the change in the spring length or displacement X point: F \u003d - RX

Another example. The mathematical pendulum of deviations from the equilibrium position is such a small angle α so that the trajectory of motion of the material point of the straight line coincides with the OX axis. At the same time, approximate equality is carried out: α ≈Sin α≈ TGα ≈X / L

Unlucky oscillations. Consider a model in which the resistance force neglected.
The amplitude and the initial phase of oscillations are determined by the initial conditions of movement, i.e. The position and speed of the material point is T \u003d 0.
Among the various types of oscillations, harmonic oscillation is the simplest form.

Thus, the material point suspended on the spring or thread makes harmonic oscillations, if not considering resistance strength.

The period of oscillations can be found from the formula: T \u003d 1 / V \u003d \u200b\u200b2P / Ω0

Flowing oscillations. In the real case, the fluctuating strengths (friction) are applied to the oscillating body, the nature of the movement changes, and the oscillation becomes attenuating.

With regard to the one-dimensional movement, the last formula will give the following form: FC \u003d - R * DX / DT

The speed of decreases of the amplitude of oscillation is determined by the attenuation coefficient: the stronger the inhibitory effect of the medium, the more ß and the faster the amplitude decreases. In practically, however, the degree of attenuation is often characterized by a logarithmic decrement of attenuation, understanding the ratio of two consecutive amplitudes, separated by a natural logarithm of the relationship of two consecutive amplitudes, a separated time interval, equal to the oscillation period, therefore, the attenuation coefficient and the logarithmic decrement of attenuation are sufficiently simple dependence: λ \u003d ßt

With severe attenuation from the formula, it can be seen that the period of oscillation is an imaginary value. The movement in this case will no longer be periodic and is called aperiodic.

Forced oscillations. Forced oscillations are called oscillations arising in the system with the participation of external force, changing in a periodic law.

Suppose that on the material point, except for the elastic strength and force of friction, the external forcing force f \u003d f0 cos ωt

The amplitude of forced oscillation is directly proportional to the amplitude of the forcing force and has a complex dependence on the attenuation coefficient of the medium and the circular frequencies of its own and forced oscillations. If ω0 and ß for the system are given, then the amplitude of the forced oscillations has the maximum value at some specific frequency of the forced force called resonant The phenomenon itself is the achievement of the maximum amplitude of the forced oscillations for the specified ω0 and ß - call resonance.

The resonant circular frequency can be found from the conditions of the minimum of the denominator in: Ωrez \u003d √ωₒ- 2ß

Mechanical resonance will burn to be both useful and harmful phenomenon. Harmful effect is mainly due to the destruction that it can cause. So, in the technique, given the different vibrations, it is necessary to provide for the possible occurrence of resonant conditions, otherwise the destruction and catastrophe may be. Bodies usually have several oscillation frequencies and, accordingly, several resonant frequencies.

Resonant phenomena under the action of external mechanical oscillations occur in the internal organs. In this, apparently, one of the reasons for the negative effects of infrasound fluctuations and vibrations on the human body.

6.Cound research methods in medicine: percussion, auscultation. Phonocardiography.

Sound may be a source of information on the state of the internal organs of a person, so in medicine such methods of studying the patient's condition as auscultation, percussion and phonocardiography are well distributed.

Auscultation

For auscultation use a stethoscope or a phonenendoscope. The phonenadoscope consists of a hollow capsule with a membrane transmitting the sound applied to the patient's body, rubber tubes go to the doctor's ear. In the capsule, there is a resonance of the air column, as a result of which the sound is enhanced and auscultation is improved. With auscultation of the lungs, breathing noises, different wheezing characteristic of diseases. You can also listen to the heart, intestines and stomach.

Percussion

In this method, the sound of individual parts of the body is listening while climbing them. Imagine a closed cavity inside some body filled with air. If you cause sound oscillations in this body, at a certain frequency of sound, the air in the cavity will begin to resonate, highlighting and enhanced the tone corresponding to the size and position of the cavity. The human body can be represented as a totality of gas-filled (lungs), liquid (internal organs) and solid (bone) volumes. When the body is impaired, oscillations occur, the frequencies of which have a wide range. From this range, some oscillations will be treated rather quickly, the other, which coincide with their own vibrations, will increase and as a result of resonance will be heard.

Phonocardiography

It is used to diagnose cardiac activity. The method is the graphical registration of the tones and the noise of the heart and their diagnostic interpretation. The phonocardiograph consists of a microphone, amplifier, system of frequency filters and a registering device.

9. Ultrasonic research methods (ultrasound) in medical diagnostics.

1) Diagnostic and Research Methods

Located methods using mainly impulsive radiation. This is an echo-detephalography - determination of tumors and swelling of the brain. Ultrasound cardiography - measurement of heart dimensions in dynamics; In ophthalmology - ultrasound location to determine the size of the eye media.

2) impact methods

Ultrasound physiotherapy is a mechanical and thermal effect on the fabric.

11. Shock wave. Getting and use of shock waves in medicine.
Shock wave - The terminal of the gap, which moves relative to the gas and with the intersection of which pressure, density, temperature and speed are leaping.
For large disturbances (explosion, supersonic motion of bodies, powerful electric discharge, etc.) The speed of the oscillating particles of the medium can be comparable at the speed of sound , shock wave arises.

Shock wave can have a significant energyThus, with a nuclear explosion on the formation of a shock wave in the environment, about 50% of the explosion energy is spent. Therefore, the shock wave, reaching biological and technical objects, is able to cause death, injury and destruction.

In medical equipment used shock waves, representing an extremely short, powerful pressure pulse with high pressure amplitudes and a small component of stretching. They are generated outside the body of the patient and are transferred deep into the body, producing the therapeutic effect provided by the specialization of the equipment model: crushing of urinary stones, treatment of pain zones and consequences of injuries of the musculoskeletal system, stimulation of the restoration of the heart muscle after myocardial infarction, smoothing cellulite formations, etc.

Everything on the planet has its own frequency. According to one of the versions, it is even based on our world. Alas, the theory is very difficult to express it within the framework of one publication, so we will be considered exclusively the frequency of oscillations as an independent action. As part of the article, it will be given a definition of this physical process, its units of measurements and the metrological component. And at the end will be considered an example of the importance in the usual life of ordinary sound. We learn what he represents and what is his nature.

What do they call the frequency of oscillations?

This implies the physical value that is used to characterize the periodic process, which is equal to the number of repetitions or the occurrences of certain events per unit of time. This indicator is calculated as the ratio of the number of incident data by the time of time for which they were committed. The own frequency of oscillations is every element of the world. Body, atom, road bridge, train, aircraft - they all commit certain movements that are so called. Let these processes are not visible to the eye, they are. Units of measurements in which the frequency of oscillations are considered to be hertz. They received their name in honor of the physics of the German origin of Herrich Hertz.

Instant frequency

The periodic signal can be characterized by an instantaneous frequency, which accurate to the coefficient is a phase change rate. It can be represented as a sum of harmonic spectral components with their permanent fluctuations.

Cyclic oscillation frequency

It is convenient to apply in theoretical physics, especially in the section about electromagnetism. Cyclic frequency (it is also called radial, circular, angular) is a physical value that is used to indicate the intensity of the origin of the oscillatory or rotational motion. The first is expressed in revolutions or fluctuations for a second. With rotational motion, the frequency is equal to the module of the angular velocity vector.

The expression of this indicator is carried out in radians for one second. The dimension of the cyclic frequency is back time. In numerical terms, it is equal to the number of oscillations or revolutions, which occurred for the number of seconds 2π. Its administration for use can significantly simplify a different spectrum of formulas in electronics and theoretical physics. The most popular example of use is the calculation of the resonant cyclic frequency of the oscillatory LC contour. Other formulas can significantly complicate.

Frequency of discrete events

Under this value, mean value, which is equal to the number of discrete events that occur in one unit of time. In theory, the indicator is usually used - second in minus the first degree. In practice, to express the frequency of impulses, the hertz usually use.

Rotation frequency

Under it, they understand the physical quantity, which is equal to the number of complete revolutions, which occur in one unit of time. It also uses the indicator - second in minus the first degree. To refer to the work done, such phrases as turnover per minute, hour, day, month, year and others are possible.

Units

What is the oscillation frequency? If you take into account the SI system, then the unit of measurement is the hertz. It was originally introduced by the International Electrotechnical Commission in 1930. And the 11th General Conference on Sighs and Measures in the 1960s secured the use of this indicator as a unit of C. What was put forward as an "ideal"? They were the frequency when one cycle is performed in one second.

But what to do with production? Arbitrary values \u200b\u200bwere fixed for them: kilocycle, megatics per second and so on. Therefore, taking a device that works with an indicator in GHz (as a computer processor), can approximately submit how much actions it makes it. It would seem how to slowly for a person the time stretches. But the technique has time to fulfill millions and even billions of operations per second during the same period. In one hour, the computer already makes so much actions that most people will not even be able to present them in numerical terms.

Metrological aspects

The oscillation frequency found its use even in metrology. Various devices have many features:

1. Measure the frequency of pulses. They are represented by electronic accounts and condenser types.
2. Determine the frequency of spectral components. There are heterodyne and resonant types.
3. The spectrum analysis is performed.
4. Reproduce the required frequency with a given accuracy. In this case, various measures can be applied: standards, synthesizers, signal generators and other technique of this direction.
5. Compare the indicators of the obtained oscillations, for this purpose a comparator or oscilloscope is used.

Sample work: sound

All the above written can be quite difficult to understand, as we used the dry language of physics. To realize the information provided, you can give an example. Everything will be painted in detail in it, based on analyzing cases from modern life. To do this, consider the most famous example of oscillations - sound. Its properties, as well as the features of the mechanical elastic oscillations in the medium, are directly dependent on the frequency.

Human hearing organs can catch the oscillations that are within 20 Hz to 20 kHz. Moreover, with age, the upper border will gradually decrease. If the frequency of sound oscillations falls below the indicator of 20 Hz (which corresponds to mi subcontrollava), then infrasound will be created. This type, which in most cases is not heard to us, people can still feel relatively. If the border is exceeded in 20 kilohertz, oscillations are generated, which are called ultrasound. If the frequency exceeds 1 GHz, then in this case we will deal with a hypersonic. If we consider such a musical instrument as piano, it can create oscillations in the range of 27.5 Hz to 4186 Hz. It should be borne in mind that the musical sound does not consist only of the main frequency - overtones, harmonics are added to it. It all defines the timbre together.

Conclusion

As you had the opportunity to know, the frequency of oscillations is an extremely important component that allows you to function our world. Thanks to her we can hear, computers work with her assistance and many other useful things are carried out. But if the frequency of oscillations exceeds the optimal limit, then certain destruction can begin. So, if you influence the processor, so that its crystal worked with twice as much indicators, it will quickly fail.

This can be brought with human life when, with high frequency, drumpipes burst. Other negative changes with the body will also occur, which will entail certain problems, up to death. Moreover, because of the peculiarities of physical nature, this process is spreading at a fairly long period of time. By the way, taking into account this factor, the military is considering new opportunities for the development of the arms of the future.

When studying this section should be borne in mind that oscillations Various physical nature is described with uniform mathematical positions. Here it is necessary to clearly understand the concepts such as harmonic oscillation, phase, phase difference, amplitude, frequency, period of oscillations.

It should be borne in mind that in any real oscillatory system there are resistances of the medium, i.e. The oscillations will be attenuating. To characterize the attenuation of oscillations, the attenuation coefficient and the logarithmic decrement of the atuchi are injected.

If oscillations are performed under the action of an external periodically changing force, then such oscillations are called forced. They will be unsuccessful. The amplitude of the forced oscillations depends on the frequency of the forcing force. When the frequency of forced oscillations approaches the frequency of its own oscillations of the amplitude of the forced oscillations increases sharply. This phenomenon is called resonance.

Moving to the study of electromagnetic waves need to clearly represent thatelectromagnetic wave - This is an electromagnetic field spreading in space. The simplest system emitting electromagnetic waves is an electric dipole. If the dipole performs harmonic oscillations, then it emits a monochromatic wave.

Table of formulas: oscillations and waves

Physical laws, formulas, variables	Formulas of oscillations and waves
Harmonic oscillation equation: where x - offset (deviation) of the oscillating value from the equilibrium position; A - amplitude; ω - circular (cyclic) frequency; α - initial phase; (ωt + α) - phase.
Communication between the period and circular frequency:
Frequency:
Circular frequency connection with frequency:
Periods of own oscillations 1) Spring pendulum: where k is the rigidity of the spring; 2) Mathematical pendulum: where L is the length of the pendulum, g - acceleration of free fall; 3) oscillatory circuit: where L is the inductance of the contour, C - capacitance of the capacitor.
Frequency of own oscillations:
Addition of oscillations of the same frequency and direction: 1) the amplitude of the resulting oscillation where a 1 and a 2 - amplitudes of the components of oscillations, α 1 and α 2 - the initial phases of the components of the oscillations; 2) the initial phase of the resulting oscillation
Flowing oscillation equations: e \u003d 2.71 ... - The basis of natural logarithms.
Sleeping oscillation amplitudes: where a 0 is amplitude at the initial moment of time; β - attenuation coefficient;
Attenuation coefficient: ibitable body where R is the coefficient of resistance of the medium, m - body weight; oscillatory circuit where R is active resistance, L - inductance of the contour.
Frequency of floating oscillations ω:
Period of floating oscillations T:
Logarithmic decrement attenuation:

In the world surrounding us, there are many phenomena and processes that, by and large, invisible because they are not, but because we simply do not notice them. They are always present and are the same imperceptible and obligatory essence of things without which our life is difficult. Each, for example, it is known that such a oscillation: in the most general form is a deviation from the state of equilibrium. Well, well, the top of the Ostankino Tower was rejected on her 5 m, and what's next? So will it freeze? Nothing like this will begin to go back, it will slip the state of equilibrium and will deviate on the other side, and so forever, until it exist. And tell me, many people really saw these quite serious fluctuations in such a huge structure? Everyone knows, hesitates, here, here, there, and day and night, in winter and summer, but somehow ... not noticeable. The reasons for the oscillatory process are another question, but its presence is an inseparable sign of all things.

All around: buildings, structures, pendulums of hours, leaves on trees, violin strings, the surface of the ocean, the legs of the chamberon ... Among the oscillations there are chaotic, which do not have strict repeatability, and cyclic, who have a full set of their Changes, and then this cycle is exactly repeated, generally speaking, infinitely long. Usually these changes imply a consistent bust of spatial coordinates, as can be observed on the example of the oscillations of the pendulum or the same tower.

The amount of oscillations per unit of time is called the frequency f \u003d 1 / t. Frequency measurement unit - Hz \u003d 1 / s. It is clear that the cyclic frequency is the parameter of the oscillations of any kind. Nevertheless, in practice, this concept is accepted, with some additions, to relate mainly to the oscillations of the rotational nature. So it happened in the technique, which is the basis of most machines, mechanisms, devices. For such oscillations, one cycle is one turnover, and then it is more convenient to use the angular parameters of movement. Based on this, the rotational movement is measured by angular units, i.e. One turn is 2π radians, and cyclic frequency ῳ \u003d 2π / T. From this expression, the connection is easily viewed with a frequency F: ῳ \u003d 2πF. This allows you to say that cyclic frequency is the number of oscillations (full revolutions) for 2π seconds.

It would seem, not in the forehead, so ... not quite so. Multipliers 2π and 2πF are used in many equations of electronics, mathematical and theoretical physics in sections, where the oscillatory processes are studied using the concept of cyclic frequency. The formula of the resonant frequency, for example, is reduced by two beings. In the case of use in the calculations of the "OB / S" unit, the angular, cyclic, frequency ῳ numerically coincides with the frequency value of F.

Oscillations, both the essence and form of the existence of matter, and its real incarnation - the subjects of our existence, are of great importance in human life. Knowledge of the laws of oscillations made it possible to create modern electronics, electrical engineering, many modern cars. Unfortunately, the oscillations do not always bring a positive effect, sometimes they bring grief and destruction. Unaccounted oscillations, the cause of many accidents, cause materials, and the cyclic frequency of resonant vibrations of bridges, dams, machine parts leads to their premature failure. The study of vibrational processes, the ability to predict the behavior of natural and technical objects in order to prevent their destruction or exit from the working state - the main task of many engineering applications, and the examination of industrial facilities and vibration resistance mechanisms is a mandatory element of operational services.