It is called harmonic analysis of sound. Harmonic analysis

Artifacts of spectral analysis and the Heisenberg uncertainty principle

In the previous lecture, we examined the problem of decomposing any sound signal into elementary harmonic signals (components), which in the future we will call atomic information elements of sound. Let us repeat the main conclusions and introduce some new notation.

We will denote the sound signal under study in the same way as in the last lecture, .

The complex spectrum of this signal is found using the Fourier transform as follows:

. (12.1)

This spectrum allows us to determine into which elementary harmonic signals of different frequencies our studied sound signal is decomposed. In other words, the spectrum describes the complete set of harmonics into which the signal under study is decomposed.

For convenience of description, instead of formula (12.1), the more expressive following notation is often used:

, (12.2)

thereby emphasizing that a time function is supplied to the input of the Fourier transform, and the output is a function that depends not on time, but on frequency.

To emphasize the complexity of the resulting spectrum, it is usually presented in one of the following forms:

where is the amplitude spectrum of harmonics, (12.4)

A is the phase spectrum of harmonics. (12.5)

If we take the right side of equation (12.3) logarithmically, we get the following expression:

It turns out that the real part of the logarithm of the complex spectrum is equal to the amplitude spectrum on a logarithmic scale (which coincides with the Weber-Fechner law), and the imaginary part of the logarithm of the complex spectrum is equal to the phase spectrum of harmonics, the values ​​of which are ( phase values) our ear does not feel. Such an interesting coincidence may be disconcerting at first, but we will not pay attention to it. But let us emphasize a fact that is fundamentally important for us now - the Fourier transform transfers any signal from the temporary physical signal domain into the information frequency space, in which the frequencies of the harmonics into which the audio signal is decomposed are invariant.

Let us denote the atomic information element of sound (harmonic) as follows:

Let's take advantage graphically, reflecting the range of audibility of harmonics with different frequencies and amplitudes, taken from the wonderful book by E. Zwicker and H. Fastl “Psychoacoustics: facts and models” (Second Edition, Springer, 1999) on page 17 (see Fig. 12.1).

If a certain sound signal consists of two harmonics:

then their position in the auditory information space may have, for example, the form shown in Fig. 12.2.

Looking at these figures, it is easier to understand why we called individual harmonic signals atomic information elements of sound. The entire auditory information space (Fig. 12.1) is limited from below by the curve of the hearing threshold, and from above by the curve of the pain threshold of sounding harmonics of different frequencies and amplitudes. This space has somewhat irregular outlines, but it is somewhat reminiscent in shape of another information space that exists in our eye - the retina. In the retina, the atomic information objects are rods and cones. Their analogue in digital information technology is piskels. This analogy is not entirely correct, since in an image all pixels (in two-dimensional space) play their role. In our sound information space, two points cannot be on the same vertical. And therefore, any sound is reflected in this space, at best, only in the form of some curved line (amplitude spectrum), starting on the left at low frequencies (about 20 Hz) and ending on the right at high frequencies (about 20 kHz).

Such reasoning looks quite beautiful and convincing, unless you take into account the real laws of nature. The fact is that, even if the original sound signal consists of only one single harmonic (of a certain frequency and amplitude), then in reality our auditory system “will not see” it as a point in the auditory information space. In reality, this point will blur somewhat. Why? Yes, because all these arguments are valid for the spectra of infinitely long-sounding harmonic signals. But our real auditory system analyzes sounds over relatively short time intervals. The length of this interval ranges from 30 to 50 ms. It turns out that our auditory system, which, like the entire neural mechanism of the brain, works discretely with a frame rate of 20-33 frames per second. Therefore, spectral analysis must be carried out frame by frame. And this leads to some unpleasant effects.

In the first stages of research and analysis of audio signals using digital information technologies, the developers simply cut the signal into separate frames, as, for example, shown in Fig. 12.3.

If one piece of this harmonic signal in a frame is sent to the Fourier transform, then we will not get a single spectral line, as shown for example in Fig. 12.1. And you will get a graph of the amplitude (logarithmic) spectrum shown in Fig. 12.4.

In Fig. 12.4 shows in red the true value of the frequency and amplitude of the harmonic signal (12.7). But the thin spectral (red) line has blurred significantly. And, worst of all, a lot of artifacts have appeared that actually reduce the usefulness of spectral analysis to no. Indeed, if each harmonic component of the sound signal introduces its own similar artifacts, then it will not be possible to distinguish true traces of sound from artifacts.

In this regard, in the 60s of the last century, many scientists made intensive attempts to improve the quality of the obtained spectra from individual frames of the audio signal. It turned out that if the frame is not roughly cut (“straight scissors”), but the sound signal itself is multiplied by some smooth function, then artifacts can be significantly suppressed.

For example, in Fig. Figure 12.5 shows an example of cutting out a piece (frame) of a signal using one period of the cosine function (this window is sometimes called the Hanning window). The logarithmic spectrum of a single harmonic signal cut out in this way is shown in Fig. 12.6. The figure clearly shows that the artifacts of spectral analysis have largely disappeared, but still remain.

In those same years, the famous researcher Hamming proposed a combination of two types of windows - rectangular and cosine - and calculated their ratio in such a way that the size of artifacts was minimal. But even this best of the best combinations of the simplest windows turned out to be, in fact, not the best in principle. The Gaussian window turned out to be the best in all window respects.

To compare the artifacts introduced by all types of time windows in Fig. Figure 12.7 shows the results of using these windows using the example of obtaining the amplitude spectrum of a single harmonic signal (12.7). And in Fig. Figure 12.8 shows the spectrum of the vowel sound “o”.

It is clearly seen from the figures that the Gaussian time window does not create artifacts. But what should be especially noted is one remarkable property of the resulting amplitude (not on a logarithmic, but on a linear scale) spectrum of the same single harmonic signal. It turns out that the graph of the resulting spectrum itself looks like a Gaussian function (see Fig. 12.9). Moreover, the half-width of the Gaussian time window is related to the half-width of the resulting spectrum by the following simple relation:

This relationship reflects the Heisenberg uncertainty principle. Tell us about Heisenberg himself. Give examples of the manifestation of the Heisenberg uncertainty principle in nuclear physics, in spectral analysis, in mathematical statistics (Student's t-test), in psychology and in social phenomena.

The Heisenberg uncertainty principle provides answers to many questions related to why the traces of some harmonic components of a signal do not differ in the spectrum. The general answer to this question can be formulated as follows. If we build a spectral film with a frame rate , then we will not be able to distinguish harmonics that differ in frequency by less than , their traces on the spectrum will merge.

Let's consider this statement using the following example.

In Fig. Figure 12.10 shows a signal about which we only know that it consists of several harmonics of different frequencies.

By cutting out one frame of this complex signal using a Gaussian time window of small width (i.e., relatively small), we obtain the amplitude spectrum shown in Fig. 12.11. Due to the fact that it is very small, the half-width of the amplitude spectrum from each harmonic will be so large that the spectral lobes from the frequencies of all harmonics will merge and overlap each other (see Fig. 12.11).

By slightly increasing the width of the Gaussian time window, we obtain another spectrum, shown in Fig. 12.12. Based on this spectrum, it can already be assumed that the signal under study contains at least two harmonic components.

Continuing to increase the width of the time window, we obtain the spectrum shown in Fig. 12.13. Then - the spectra in Fig. 12.14 and 12.15. Looking at the last figure, we can say with a high degree of confidence that the signal in Fig. 12.10 consists of three separate components. After such large-scale illustrations, let’s return to the issue of searching for harmonic components in real speech signals.

It should be emphasized here that there are no pure harmonic components in a real speech signal. In other words, we do not produce harmonic components of type (12.7). But, nevertheless, quasi-harmonic components are still present in speech.

The only quasi-harmonic components in the speech signal are damped harmonics that occur in the resonator (vocal tract) after clapping vocal cords. The relative arrangement of the frequencies of these damped harmonics determines the formant structure of the speech signal. A synthesized example of a damped harmonic signal is shown in Fig. 12.16. If you cut a small fragment from this signal using the Gaussian time window and send it to the Fourier transform, you will get the amplitude spectrum (on a logarithmic scale) shown in Fig. 12.17.

If we cut out from a real speech signal one period between two clap of the vocal cords (see Fig. 12.18), and somewhere in the middle of this fragment we place a time window for spectral estimation, then we will obtain the amplitude spectrum shown in Fig. 12.19. In this figure, the red lines show the values ​​of the manifested frequencies of complex resonant oscillations of the vocal tract. This figure clearly shows that with the chosen small width of the spectral estimation time window, not all resonant frequencies of the vocal tract were clearly visible in the spectrum.

But it's inevitable. In this regard, the following recommendations can be formulated for visualizing traces of resonant frequencies of the vocal tract. The frame rate of the spectral film should be an order of magnitude (times 10) greater than the frequency of the vocal cords. But it is impossible to increase the frame rate of the spectral film indefinitely, since due to the Heisenberg uncertainty principle, traces of the formants on the sonogram will begin to merge.

What would the spectrum on the previous slide look like if a rectangular window cut out exactly N periods of the harmonic signal? Remember the Fourier series.

Artifact - [from lat. arte artificially + factus made] – biol. formations or processes that sometimes arise during the study of a biological object due to the influence of the research conditions themselves on it.

This function is called variously: weighting function, windowing function, weighing function, or weighting window.

Harmonic analysis of sound is called

A. establishing the number of tones that make up a complex sound.

B. establishing the frequencies and amplitudes of the tones that make up a complex sound.

Correct answer:

1) only A

2) only B

4) neither A nor B

Sound Analysis

Using sets of acoustic resonators, you can determine which tones are part of a given sound and what their amplitudes are. This determination of the spectrum of a complex sound is called its harmonic analysis.

Previously, sound analysis was performed using resonators, which are hollow balls of different sizes, with an open extension inserted into the ear, and a hole with opposite side. For sound analysis, it is essential that whenever the analyzed sound contains a tone whose frequency is equal to the frequency of the resonator, the latter begins to sound loudly in this tone.

Such methods of analysis, however, are very imprecise and laborious. Currently, they are being replaced by much more advanced, accurate and fast electroacoustic methods. Their essence boils down to the fact that an acoustic vibration is first converted into an electrical vibration, maintaining the same shape, and therefore having the same spectrum, and then this vibration is analyzed by electrical methods.

One of the significant results of harmonic analysis concerns the sounds of our speech. We can recognize a person's voice by timbre. But how do sound vibrations differ when the same person sings different vowels on the same note? In other words, how do the periodic air vibrations caused by the vocal apparatus differ in these cases? different positions lips and tongue and changes in the shape of the mouth and pharynx? Obviously, in the vowel spectra there must be some features characteristic of each vowel sound, in addition to those features that create the timbre of a given person's voice. Harmonic analysis vowels confirms this assumption, namely: vowel sounds are characterized by the presence in their spectra of overtone areas with large amplitude, and these areas always lie at the same frequencies for each vowel, regardless of the height of the sung vowel sound.

What physical phenomenon underlies the electroacoustic method of sound analysis?

1) conversion of electrical vibrations into sound

2) decomposition of sound vibrations into a spectrum

3) resonance

4) conversion of sound vibrations into electrical ones

Solution.

The idea of ​​the electroacoustic method of sound analysis is that the sound vibrations under study act on the microphone membrane and cause its periodic movement. The membrane is connected to a load, the resistance of which changes in accordance with the law of movement of the membrane. Since the resistance changes while the current remains the same, the voltage also changes. They say that modulation of the electrical signal occurs - electrical oscillations arise. Thus, the electroacoustic method of sound analysis is based on the conversion of sound vibrations into electrical ones.

The correct answer is listed at number 4.

The application of the harmonic analysis method to the study of acoustic phenomena made it possible to resolve many theoretical and practical problems. One of the difficult questions of acoustics is the question of the peculiarities of the perception of human speech.

The physical characteristics of sound vibrations are frequency, amplitude and initial phase of vibrations. For the perception of sound by the human ear, only two things are important: physical characteristics- frequency and amplitude of oscillations.

But if this is really the case, then how do we recognize the same vowels a, o, u, etc. in speech different people? After all, one person speaks in bass, another in tenor, another in soprano; therefore, the pitch of the sound, i.e., the frequency of sound vibrations, when pronouncing the same vowel turns out to be different for different people. We can sing a whole octave on the same vowel a, changing the frequency of sound vibrations by half, and still we learn that it is a, but not o or u.

Our perception of vowels does not change when the volume of the sound changes, that is, when the amplitude of vibrations changes. We confidently distinguish loudly and quietly spoken a from i, u, o, e.

An explanation for this remarkable feature of human speech is provided by the results of an analysis of the spectrum of sound vibrations that arise when pronouncing vowels.

Analysis of the spectrum of sound vibrations can be carried out in various ways. The simplest of these is to use a set of acoustic resonators called Helmholtz resonators.

An acoustic resonator is a cavity, usually spherical

form communicating with the external environment through a small hole. As Helmholtz showed, the natural frequency of oscillations of the air enclosed in such a cavity, to a first approximation, does not depend on the shape of the cavity and for the case of a round hole is determined by the formula:

where is the natural frequency of the resonator; - speed of sound in air; - hole diameter; V is the volume of the resonator.

If you have a set of Helmholtz resonators with different natural frequencies, then to determine the spectral composition of sound from some source, you need to alternately bring different resonators to your ear and determine by ear the onset of resonance by increasing the sound volume. Based on such experiments, it can be argued that complex acoustic vibrations contain harmonic components, which are the natural frequencies of the resonators in which the phenomenon of resonance was observed.

This method of determining the spectral composition of sound is too labor-intensive and not very reliable. One could try to improve it: use the entire set of resonators at once, providing each of them with a microphone for converting sound vibrations into electrical vibrations and a device for measuring the current strength at the microphone output. To obtain information about the spectrum of harmonic components of complex sound vibrations using such a device, it is enough to take readings from all measuring instruments at the exit.

However, this method is not used in practice, since more convenient and reliable methods for spectral analysis of sound have been developed. The essence of the most common of them is as follows. Using a microphone, the studied sound frequency air pressure fluctuations are converted into electrical voltage fluctuations at the microphone output. If the quality of the microphone is high enough, then the dependence of the voltage at the microphone output on time is expressed by the same function as the change in sound pressure over time. Then the analysis of the spectrum of sound vibrations can be replaced by the analysis of the spectrum of electrical vibrations. Analysis of the spectrum of electrical vibrations of sound frequency is technically simpler, and the measurement results turn out to be much more accurate. The operating principle of the corresponding analyzer is also based on the phenomenon of resonance, but not in mechanical systems, but in electrical circuits.

The application of the spectrum analysis method to the study of human speech made it possible to discover that when a person pronounces, for example, the vowel a at a pitch up to the first octave

sound vibrations of a complex frequency spectrum arise. In addition to oscillations with a frequency of 261.6 Hz, corresponding to a tone up to the first octave, a number of harmonics of higher frequencies are found in them. When the tone in which a vowel is pronounced changes, changes occur in the spectrum of sound vibrations. The amplitude of the harmonic with a frequency of 261.6 Hz drops to zero, and a harmonic appears corresponding to the tone at which the vowel is now pronounced, but a number of other harmonics do not change their amplitude. A stable group of harmonics characteristic of a given sound is called its formant.

If you play a record of a song performed at 78 rpm, intended to be played at 33 rpm, the melody of the song will remain unchanged, but the sounds and words will not only sound higher pitched, but will become unrecognizable. The reason for this phenomenon is that the frequencies of all the harmonic components of each sound change.

We come to the conclusion that the human brain, based on signals received through nerve fibers from the hearing aid, is capable of determining not only the frequency and amplitude of sound vibrations, but also the spectral composition of complex sound vibrations, as if performing the work of a spectrum analyzer of the harmonic components of non-harmonic vibrations.

A person is able to recognize the voices of familiar people, distinguish sounds of the same tone obtained using various musical instruments. This ability is also based on the difference in the spectral composition of sounds of the same fundamental tone from different sources. The presence in their spectrum of stable groups - formants of harmonic components - gives the sound of each musical instrument characteristic “coloring” called timbre of sound.

1. Give examples of non-harmonic vibrations.

2. What is the essence of the harmonic analysis method?

3. What are practical applications harmonic analysis method?

4. How do different vowel sounds differ from each other?

5. How is harmonic analysis of sound carried out in practice?

6. What is the timbre of sound?

In practice, it is more often necessary to solve the opposite problem in relation to the one discussed above - the decomposition of a certain signal into its constituent harmonic oscillations. In a course of mathematical analysis, a similar problem is traditionally solved by expanding a given function into a Fourier series, i.e., into a series of the form:

Where i =1,2,3….

A practical Fourier series expansion called harmonic analysis , consists in finding the quantities a 1 ,a 2 ,…,a i , b 1 ,b 2 ,…,b i , called Fourier coefficients. Based on the value of these coefficients, one can judge the share in the studied function of harmonic oscillations of the corresponding frequency, a multiple of ω . Frequency ω is called the fundamental or carrier frequency, and the frequencies 2ω, 3ω,…i·ω – respectively 2nd harmonic, 3rd harmonic, i th harmonic. The use of mathematical analysis methods makes it possible to expand most functions that describe real physical processes into Fourier series. The use of this powerful mathematical apparatus is possible under the condition of an analytical description of the function under study, which is an independent and often not a simple task.

The task of harmonic analysis can be formulated as a search in a real signal for the presence of a particular frequency. For example, there are methods for determining the rotation speed of a turbocharger rotor based on an analysis of the sound accompanying its operation. The characteristic whistle heard when a turbocharged engine is running is caused by air vibrations due to the movement of the compressor impeller blades. The frequency of this sound and the speed of rotation of the impeller are proportional. When using analog measuring equipment in these cases, they proceed something like this: simultaneously with the reproduction of the recorded signal, oscillations of a known frequency are created using a generator, moving them through the range under study until resonance occurs. The frequency of the generator corresponding to the resonance will be equal to the frequency of the signal under study.

The introduction of digital technology into measurement practice makes it possible to solve such problems using calculation methods. Before considering the main ideas inherent in these calculations, we will show the distinctive features of the digital representation of the signal.

Discrete methods of harmonic analysis

Rice. 18. Quantization by amplitude and time

A – original signal; b – quantization result;

V , G – saved data

When using digital equipment, a real continuous signal (Fig. 18, A) is represented by a set of points, or more precisely by the values ​​of their coordinates. To do this, the original signal, coming, for example, from a microphone or accelerometer, is quantized in time and amplitude (Fig. 18, b). In other words, the measurement and storage of the signal value occurs discretely after a certain time interval Δt , and the value itself at the time of measurement is rounded to the nearest possible value. Time Δt called time sampling , which is inversely related to the sampling frequency.

The number of intervals into which the double amplitude of the maximum permissible signal is divided is determined by the bit capacity of the equipment. It is obvious that for digital electronics, which ultimately operates with Boolean values ​​(“one” or “zero”), all possible bit depth values ​​will be determined as 2 n. When we say that the sound card of our computer is 16-bit, this means that the entire permissible interval of the input voltage value (the y-axis in Fig. 11) will be divided into 2 16 = 65536 equal intervals.

As can be seen from the figure, with a digital method of measuring and storing data, some of the original information will be lost. To increase the accuracy of measurements, the bit depth and sampling frequency of the converting equipment should be increased.

Let's return to the task at hand - determining the presence of a certain frequency in an arbitrary signal. For greater clarity of the techniques used, consider a signal that is the sum of two harmonic oscillations: q=sin 2t +sin 5t , specified with discreteness Δt=0.2(Fig. 19). The table in the figure shows the values ​​of the resulting function, which we will further consider as an example of some arbitrary signal.

Rice. 19. Signal under study

To check the presence of the frequency of interest to us in the signal under study, we multiply the original function by the dependence of the change in the vibrational value at the frequency being tested. Then we add (numerically integrate) the resulting function. We will multiply and sum signals over a certain interval - the period of the carrier (fundamental) frequency. When choosing the value of the fundamental frequency, it must be borne in mind that it is possible to check only a greater one in relation to the fundamental one, in n times the frequency. Let's choose as the main frequency ω =1, which corresponds to the period.

Let's start the test immediately with the “correct” (present in the signal) frequency y n =sin2x. In Fig. 20 the actions described above are presented graphically and numerically. It should be noted that the result of the multiplication passes mainly above the x-axis, and therefore the sum is noticeably greater than zero (15.704>0). A similar result would be obtained by multiplying the original signal by q n =sin5t(the fifth harmonic is also present in the signal under study). Moreover, the greater the amplitude of the tested signal in the test signal, the greater the result of calculating the sum.

Rice. 20. Checking the presence of a component in the signal under study

q n = sin2t

Now let's perform the same actions for a frequency that is not present in the signal under study, for example, for the third harmonic (Fig. 21).

Rice. 21. Checking the presence of a component in the signal under study

q n =sin3t

In this case, the curve of the multiplication result (Fig. 21) passes both in the region of positive and negative amplitudes. Numerical integration of this function will give a result close to zero ( ∑ =-0.006), which indicates the absence of this frequency in the signal under study or, in other words, the amplitude of the harmonic under study is close to zero. Theoretically we should have gotten zero. The error is caused by limitations of discrete methods due to the finite bit depth and sampling frequency. By repeating the steps described above the required number of times, you can find out the presence and level of a signal of any frequency that is a multiple of the carrier.

Without going into details, we can say that approximately the same actions are performed in the case of the so-called discrete Fourier transform .

In the example considered, for greater clarity and simplicity, all signals had the same (zero) initial phase shift. To take into account possible different initial phase angles, the actions described above are performed with complex numbers.

There are many known discrete Fourier transform algorithms. The result of the transformation - the spectrum - is often presented not as a line, but as a continuous one. In Fig. Figure 22 shows both variants of the spectra for the signal studied in the example considered.

Rice. 22. Spectrum options

Indeed, if in the example considered above we had performed the test not only for frequencies strictly multiple of the fundamental one, but also in the vicinity of multiple frequencies, we would have found that the method shows the presence of these harmonic oscillations with an amplitude greater than zero. The use of a continuous spectrum in signal research is also justified by the fact that the choice of the fundamental frequency in research is largely random.

I DIDN'T SEE A DISCUSSION OF THESE TASKS! I WILL ASK VERBALLY!

Request 20 No. 44. The electric arc is

A. from the light of electricity connected to a current source.

B. electric discharge in gas.

Correct answer

1) only A

2) only B

4) neither A nor B

Electric arc

An electric arc is one of the types of gas discharge. You can get it in the following way. In the state, two coal rods are fastened with pointed ends to each other and connected to a current source . When the coals are brought into contact and then moved slightly, a bright light appears between the ends of the coals. the flame, and the coals themselves grow white. The arc burns steadily if a constant electric current flows through it. In this case, one electrode is always positive (anode), and the other is positive (cathode). Between the electricity there is a column of hot gas, good for electricity. Po-living coal, having a higher temperature, burns faster, and a deepening is formed in it -le-nie - po-lo-zhi-tel-ny cra-ter. The temperature in the air at atmospheric pressure reaches up to 4,000 °C.

An arc can also burn between electrical metals. At the same time, the electricity melts and is quickly consumed, which consumes a lot of energy. For this reason, the temperature of metal-li-che-electricity is usually lower than coal (2,000— 2,500 °C). When the arc burned in gas at high pressure (about 2 10 6 Pa), the temperature was achieved up to 5,900 °C, i.e. up to the temperature at the top of the Sun. A column of gases or vapors, through which a discharge occurs, has an even higher temperature - up to 6,000-7,000 °C. This is why almost all known substances melt into arcs in the column and turn into steam.

To maintain the arc, you need a little voltage, the arc burns when there is voltage on its electric dah 40 V. The current strength in the arc is quite significant, but the opposite is not significant; next, a luminous gas column conducts a good electric current. The ionization of gas molecules in the space between the electrons is caused by their impact on the electrons, used let-my-house-arcs. The large number of uses of elec- trons is ensured by the fact that the cathode is heated to a very high temperature -pe-ra-tu-ry. When, in order to spark the arc, the coals are brought into contact, then in the place of contact, about-la-da-yu -We have a very large amount of heat, you have a huge amount of warmth. That's why the ends of the coals heat up very much, and this is enough so that when they move apart, an arc breaks out between them . Subsequently, the cathode of the arc is kept in a heated state by the current itself passing through the arc.

Request 20 No. 71. Gar-mo-no-che-ana-li-z sound na-zy-va-yut

A. establishing the number of tones included in the composition of a complex sound.

B. establishment of frequencies and amplitudes of tones included in the composition of a complex sound.

Correct answer:

1) only A

2) only B

4) neither A nor B

Analysis of sound

With the help of acoustic signals, you can establish which tones are included in a given sound and how-to-you am-pl-tu-dy them. This establishment of the spectrum of a complex sound calls for its harmonic analysis.

Previously, the analysis of sound was carried out with the help of re-zo-on-ditch, representing hollow balls of different sizes -ra, having an open-open drain, inserted into the ear, and a hole with a pro-ti-false side -us. For the analysis of sound, it is essential that whenever an ana-li-zi-ru-e sound contains a tone, often -to-ro-go is equal to the frequency of re-zo-na-to-ra, the last-chi-na-is loud in this tone.

Such methods are, however, very inaccurate and bloody. At the present time, they are much more advanced, accurate and fast electrically. aku-sti-che-ski-mi me-to-da-mi. Their essence boils down to the fact that the acoustic co-le-ba-nie of sleep transforms into an electric co-co -le-ba-nie with co-storage of the same shape, and therefore, having the same spectrum, and then this co-le-ba-nie ana-li-zi-ru-et-sya elek-tri-che-ski-mi me-to-da-mi.

One of the essential results of the gar-mo-none-of-any-ana-li-for-the-sounds of our speech. By timbre we can recognize a person's voice. But how different are the sounds when the same person sings different vowels on the same note? Other words, what are the differences in these cases between the pe-ri-o-di-che-k-le-ba-niya air ha, you-you-s-my-go-lo-with-you a-pa-ra-tom with different lips and tongue and from-me-no-no- How are the shapes of the mouth and pharynx? Obviously, in the spectra of vowels there must be some special features, characteristic for each vowel sound, in addition to those special-ben-no-stey, which create the timbre of the voice of a given person. Gar-mo-ni-che-analysis of vowels confirms this pre-position, namely: vowel sounds ha-rak-te-ri- zu-yut-sya na-li-chi-em in their spec-tras of the regions are ob-er-new with a large amplitude, and these regions lie for each the vowel is always at the same frequency, not behind the sound of the vowel sound.

Request 20 No. 98. In mass spectrograph

1) electric and magnetic fields serve to accelerate the charge of the part

2) electric and magnetic fields serve to change the direction of movement of the charged part tsy

3) the electric field serves to accelerate the charging part, and the magnetic field serves to change the right-hand direction of her movement

4) the electric field serves to change the direction of movement of the charged part, and the magnet The field serves to accelerate it

Mass spectrograph

A mass spectrograph is a device for dividing ions by their value from their charge to mass. In the simplest mo-di-fi-ka-tion, the scheme of the pri-bo-ra appears on the ri-sun-ke.

Is-the-next-example of special-tsi-al-ny-mi me-to-da-mi (with-pa-re-ni-em, electronic shock) re-transformed into a gas-formed state, then the ion-formed gas is formed into exactly 1. Then the ions are accelerated by an electric field and formed into a narrow beam in an accelerating device 2, after which, through a narrow entrance slot, they enter chamber 3, in which a single magnetic field is created. The magnetic field changes the trajectory of the movement of particles. Under the influence of the Lorentz force, the ions begin to move along an arc of a circle and move to screen 4, where the re-gi-stri -ru-et-their place in-pa-da-niya. Registration methods can be different: photo-graphic, electronic, etc. Ra-di-ustra -ek-to-rii is determined by the form:

Where U- electric voltage accelerating the electric field; B- induction of magnetic field; m And q- accordingly, the mass and charge of the particle.

Since the radius of the tra-ek-to-rii depends on the mass and charge of the ion, then different ions appear on the screen in different races -I'm based on the source that allows me to separate them and analyze the composition of the sample.

At the present time, many types of mass spectrometers are being developed, the working principles of which are that is from the considerations above. From-go-tav-li-va-yut-sya, for example, di-na-mi-che-mass-spectro-meters, in which masses are studied The number of ions is determined by the time of flight from the source to the re-gi-stri-ru-y device.