Determining the frequency of a tuning fork using the beating method. Conditions for adequate modeling

If you bring the magnetic needle close, it will tend to become perpendicular to the plane passing through the axis of the conductor and the center of rotation of the needle. This indicates that special forces act on the arrow, which are called magnetic forces . In addition to the effect on the magnetic needle, the magnetic field affects moving charged particles and current-carrying conductors located in the magnetic field. In conductors moving in a magnetic field, or in stationary conductors located in an alternating magnetic field, an inductive electromotive force (emf) arises.

A magnetic field

According to the above, we can give following definition magnetic field.

One of the two sides is called a magnetic field electromagnetic field, excited electric charges moving particles and a change in the electric field and is characterized by a force effect on moving infected particles, and therefore on electric currents.

If you pass a thick conductor through cardboard and pass an electric current through it, then the steel filings poured onto the cardboard will be located around the conductor in concentric circles, representing in this case so-called magnetic induction lines (Figure 1). We can move the cardboard up or down the conductor, but the location of the steel filings will not change. Consequently, a magnetic field arises around the conductor along its entire length.

If you put small ones on cardboard magnetic needles, then by changing the direction of the current in the conductor, you can see that the magnetic needles will rotate (Figure 2). This shows that the direction of magnetic induction lines changes with the direction of current in the conductor.

Magnetic induction lines around a current-carrying conductor have the following properties: 1) magnetic induction lines straight conductor have the shape of concentric circles; 2) the closer to the conductor, the denser the magnetic induction lines are located; 3) magnetic induction (field intensity) depends on the magnitude of the current in the conductor; 4) the direction of magnetic induction lines depends on the direction of the current in the conductor.

To show the direction of the current in the conductor shown in section, a symbol has been adopted, which we will use in the future. If you mentally place an arrow in the conductor in the direction of the current (Figure 3), then in the conductor in which the current is directed away from us, we will see the tail of the arrow’s feathers (a cross); if the current is directed towards us, we will see the tip of an arrow (point).

Figure 3. Symbol direction of current in conductors

The gimlet rule allows you to determine the direction of magnetic induction lines around a current-carrying conductor. If a gimlet (corkscrew) with a right-hand thread moves forward in the direction of the current, then the direction of rotation of the handle will coincide with the direction of the magnetic induction lines around the conductor (Figure 4).

A magnetic needle introduced into the magnetic field of a current-carrying conductor is located along the magnetic induction lines. Therefore, to determine its location, you can also use the “gimlet rule” (Figure 5). The magnetic field is one of the most important manifestations electric current and cannot be obtained independently and separately from the current.

Figure 4. Determining the direction of magnetic induction lines around a current-carrying conductor using the “gimlet rule” Figure 5. Determining the direction of deviation of a magnetic needle brought to a conductor with current, according to the “gimlet rule”

Magnetic induction

A magnetic field is characterized by a magnetic induction vector, which therefore has a certain magnitude and a certain direction in space.

A quantitative expression for magnetic induction as a result of generalization of experimental data was established by Biot and Savart (Figure 6). Measuring the magnetic fields of electric currents by the deviation of the magnetic needle various sizes and shape, both scientists came to the conclusion that every current element creates a magnetic field at some distance from itself, the magnetic induction of which is Δ B is directly proportional to the length Δ l this element, the magnitude of the flowing current I, the sine of the angle α between the direction of the current and the radius vector connecting the field point of interest to us with a given current element, and is inversely proportional to the square of the length of this radius vector r:

Where K– coefficient depending on magnetic properties environment and on the chosen system of units.

In the absolute practical rationalized system of units of ICSA

where µ 0 – magnetic permeability of vacuum or magnetic constant in the MCSA system:

µ 0 = 4 × π × 10 -7 (henry/meter);

Henry (gn) – unit of inductance; 1 gn = 1 ohm × sec.

µ – relative magnetic permeability– a dimensionless coefficient showing how many times the magnetic permeability of a given material is greater than the magnetic permeability of vacuum.

The dimension of magnetic induction can be found using the formula

Volt-second is also called Weber (wb):

In practice, there is a smaller unit of magnetic induction - gauss (gs):

Biot-Savart's law allows us to calculate the magnetic induction of an infinitely long straight conductor:

Where A– the distance from the conductor to the point where the magnetic induction is determined.

Magnetic field strength

Ratio of magnetic induction to product magnetic permeabilitiesµ × µ 0 is called magnetic field strength and is designated by the letter H:

B = H × µ × µ 0 .

The last equation relates the two magnetic quantities: induction and magnetic field strength.

Let's find the dimension H:

Sometimes another unit of measurement of magnetic field strength is used - Oersted (er):

1 er = 79,6 A/m ≈ 80 A/m ≈ 0,8 A/cm .

Magnetic field strength H, like magnetic induction B, is a vector quantity.

A line tangent to each point of which coincides with the direction of the magnetic induction vector is called magnetic induction line or magnetic induction line.

Magnetic flux

The product of magnetic induction and the size of the area, perpendicular to the direction field (magnetic induction vector) is called flux of the magnetic induction vector or simply magnetic flux and is denoted by the letter F:

F = B × S .

Dimension magnetic flux:

that is, magnetic flux is measured in volt-seconds or webers.

The smaller unit of magnetic flux is Maxwell (mks):

1 wb = 108 mks.
1mks = 1 gs× 1 cm 2.

Video 1. Ampere's hypothesis

Video 1. Ampere's hypothesis

Video 2. Magnetism and electromagnetism

Hello, dear readers. Always and at all times, watchmakers, when creating mechanisms, tried to improve the accuracy of watches using various technologies. And in short period between the 50s, when they reigned supreme mechanical watches and the beginning of the 70s, when the new kings of precision, quartz watches, ascended the throne, the star of tuning fork watches sparkled brightly in the sky and disappeared. In the fifties, there were already predecessors to quartz watches, but they were far from being commercialized. Bulova decided to take an alternative route, and decisive role Swiss engineer Max Hetzel played a role in this, who at that time joined the company’s office located in the city of Biel.

In March 1952, watchmakers from Elgin and Lip introduced electric watches. This watch has been hailed as the greatest breakthrough in watchmaking in 450 years.

Arde Bulova, who was the president of Bulova watches at the time, asked Max Hetzel to study this new watch. The president was concerned that his company might lose market share if it did not also produce battery-powered watches. Max Hetzel reported his findings to Bulova management in April 1952. In his report, he stated that these new galvanic cell watches still used a conventional balance wheel and this could not lead to a significant improvement in accuracy. His report predicted that the newly developed transistor would be a key component for future electronic clocks.

Bulova began developing the Accutron in 1952. Accutron should have been electronic watch, which will guarantee an accuracy of about 2 seconds per day or 1 minute per month. The secret of this accuracy will be a tuning fork, which will divide each second into hundreds of equal parts. In March 1953, Hetzel received the first low voltage transistor (Raytheon CK 722) from Bulova headquarters. This transistor and the tuning fork frequency filter that Hetzel had previously developed allowed him to build the first simple tuning fork oscillator on a piece of wood! It operated with a frequency of 200 Hz and was powered by a voltage of 1.5 V. The wheel had 120 teeth 1/10 mm long. The first prototype of the watch movement was made in Switzerland in 1955. In 1959, Max Hetzel and William Bennett completed development of the Accutron 214 at Bulova headquarters in New York.

So what are tuning fork clocks? As we know, a tuning fork looks like a fork with two prongs. When struck, the legs of the tuning fork begin to vibrate, with a frequency that depends on the elasticity of the material and geometric shape legs The ability for long, stable vibrations made it possible to use a tuning fork for tuning musical instruments and not only. For example, a tuning fork was used to adjust the speed of engines. To do this, stripes or squares were applied to the rotating part, and there were “window” covers at the ends of the tuning forks. And if you look at the rotating part with the applied markers through the “window” of a tuning fork oscillating at a certain frequency, you could see how the white mark either stood still at the correct rotation speed, or moved up or down when there were deviations in engine operation. It is this ability to stable oscillations of the tuning fork that has found application in the mechanism of the watch in question. Typically, mechanical wristwatches use a balance regulator (balance regulator). The balance is the central unit that regulates the course of the oscillatory system. In a tuning fork clock, the role of a regulator is played by a miniature tuning fork. The technical embodiment of this system is a fusion of mechanics and electronics. Electrical diagram tuning fork clock is quite simple. Without going into details, it consists of a transistor, a resistor and a capacitor. The watch is powered by a galvanic cell. Magnetic circuits are installed at the ends of the legs of a miniature tuning fork. At the bottom of the magnetic circuits are fixed permanent magnets. The fork itself is rigidly attached to the platinum. Also attached to the watch plate is a plastic frame with two coils wound on it - a pulse and an excitation coil. The coils are connected in series.

The tuning fork mechanism works as follows: after power is supplied from the galvanic element, permanent magnets with magnetic circuits located on the legs of a miniature tuning fork begin to oscillate, moving along the coils (pulse and excitation coils). An EMF (electromotive force) arises in the excitation coil, which unlocks the transition of the transistor. The current from the galvanic element through the collector-emitter junction of the transistor is supplied to the pulse coil. The magnetic field of the coil affects the tuning fork, giving it an impulse, thereby maintaining constant vibrations of the tuning fork legs. The wires wound on the reel were the thickness of a human hair. Their total length was 200 meters. The vibration frequency of the legs of a miniature tuning fork depends on the elasticity of the material and the geometric shape of the legs. The vibration of a tuning fork cannot be seen; as a rule, the vibration frequency of a tuning fork is 360Hz.

A pusher is attached to one of the legs of the tuning fork, transmitting oscillatory movements tuning fork to ratchet mechanism. The running wheel of the ratchet mechanism is in constant mesh with other gears, driving the entire clock mechanism. The ratchet is secured by a spring against rotation. The mechanism was very small. For example, a ratchet wheel tooth measured 0.025 mm wide and 0.01 mm high. The wheel itself was 2.4 mm in diameter and had 300 teeth. Due to the fact that the clock made a slight hum or squeak, it became known as the “singing clock.” More for of this type The watch was characterized by a smooth movement of the second hand.

Tuning fork clock circuit: T - transistor; R - resistor; C - capacitor; L1 - release winding; L2 - pulse winding; E - power supply ( galvanic cell); 1 - tuning fork; 2 - ratchet mechanism; 3 - wheel drive; 4 - arrows.

Actually, the first watch models entered the market in 1960. Bulova gave them the name Accutron, which comes from “Accu-” for accuracy and “-tron” for electronic. The watch became very popular; it seemed to buyers simply a technical miracle. Their accuracy was plus or minus 2 seconds per day. At that time it was excellent result for wristwatches. The clock was powered by a 1.35 Volt battery, which is not easy to find these days. The modern standard is 1.5 Volts.

Accutron Spaceview was an unexpected success. This model was not actually intended for sale, but was supplied to watch stores as an exhibition piece. Its skeletonized dial was meant to showcase an advanced mechanism. But buyers really liked their futuristic look, especially since it was the time space race and dawn science fiction, and they desperately asked to sell them Spaceview. Bulova listened to its customers and released the Accutron Spaceview.


In 1968, Heinz Haber, a German physicist and aerospace medical consultant, demonstrated how space technology may affect daily life– the audience heard the sound of his own Accutron SpaceView through the microphone.

Naturally, the military was also interested in accurate clock. Accutron watches with 214 caliber were supplied to the Air Force.

However, they were not wristwatches, these watches were intended to be mounted on the dashboard. Special 24-hour Accutrons were also installed on the dashboard of American spacecraft. For the first time this happened within space mission Gemini. And in 1969, such Accutron instruments were left on the Moon by Apollo 11 astronauts Neil Armstrong and Edwin Aldrin, and now they rest in the Sea of ​​Tranquility.

In 1962, the Accutron 214 became the first wristwatch certified for use by railroad personnel.


In 1964, President Lyndon Johnson approved the Bulova Accutron as an official White House "Gift of State" gift to foreign leaders.

But not Bulov’s alone. In the Soviet Union, it was decided to make their own version of the tuning fork clock. In 1962, the Second Moscow Watch Factory produced the “Glory Transistor” with caliber 2937. The Leipzig Fair brought this watch gold medal. The watch did not have a traditional crown; the hands were moved by a folding “earring” on the case back. Actually like Accutron Spaceview.

Omega had many interesting models, such as the famous 300hz series, which used a cosmetically modified ETA-ESA 9162 movement.

Omega Caliber 1250 = ESA 9162 (date only)

Omega Caliber 1255 = ESA 9210 (chronograph day and date)

Omega Caliber 1260 = ESA 9164 (day and date)


The culmination was the Omega 1220 MegaSonic, produced in 1973-1974. MegaSonic clocked at 720 Hz, versus the standard 360. The ratchet wheel is smaller, unlike other tuning fork clocks. With a diameter of 1.2 mm, this wheel has 180 teeth (versus 2.4 mm and 300 teeth in 360 Hz mechanisms). What was new was that the electromagnetic clutch transmitted energy without any contact. This technology is rare, almost unique today. MegaSonic is one of the rarest tuning fork watches. MegaSonic was produced with two versions of mechanisms: Caliber 1220 (date) and 1230 (day and date).

The Omega f300 Speedsonic chronograph released in 1972 on the ESA 9162 movement was very interesting.

Tuning fork watches were also produced by Eterna, Longines, Certina, Titus, Tissot, Zenith and many others.


The mechanisms of these watches are pleasant to look at, they compare favorably with the plastic squalor of most modern mass-produced quartz calibers.

With the advent of quartz, the song of the tuning fork “singing” clock was over. Bulova and ETA stopped producing tuning fork movements in 1977. Quartz watch were simpler, more reliable, and most importantly more accurate and at the same time cheaper. Tuning fork clock They were very “gluttonous”; the battery had to be changed two or even three times a year. The multi-tooth gear was difficult to manufacture, and at the same time it had a short resource. Weak point These watches had a tuning fork attached to the base, usually done by spot welding. But still, for its time, these watches were a real breakthrough and today attract watch lovers thanks to the interesting technical part and, of course, history.

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Resonance phenomena can be observed on mechanical vibrations any frequency, in particular on sound vibrations. We have an example of sound or acoustic resonance in the following experiment.

Let's place two identical tuning forks next to each other, turning the holes of the boxes on which they are mounted towards each other (Fig. 40). Boxes are needed because they amplify the sound of tuning forks. This occurs due to resonance between the tuning fork and the column of air enclosed in the box; hence the boxes are called resonators or resonant boxes. We will explain the operation of these boxes in more detail below when studying the distribution sound waves in the air. In the experiment that we will now analyze, the role of the boxes is purely auxiliary.

Rice. 40. Resonance of tuning forks

Let's hit one of the tuning forks and then muffle it with our fingers. We will hear how the second tuning fork sounds.

Let's take two different tuning forks, i.e. different heights tone, and repeat the experiment. Now each of the tuning forks will no longer respond to the sound of another tuning fork.

It is not difficult to explain this result. The vibrations of one tuning fork (1) act through the air with some force on the second tuning fork (2), causing it to perform forced oscillations. Since tuning fork 1 performs a harmonic oscillation, the force acting on tuning fork 2 will change according to the law of harmonic oscillation with the frequency of tuning fork 1. If the frequency of the force is the same as the natural frequency of tuning fork 2, then resonance occurs - tuning fork 2 swings strongly. If the frequency of the force is different, then the forced vibrations of tuning fork 2 will be so weak that we will not hear them.

Since tuning forks have very little attenuation, their resonance is sharp (§ 14). Therefore, even a small difference between the frequencies of the tuning forks leads to the fact that one ceases to respond to the vibrations of the other. It is enough, for example, to glue pieces of plasticine or wax to the legs of one of two identical tuning forks, and the tuning forks will already be out of tune, there will be no resonance.

We see that all phenomena during forced oscillations occur with tuning forks in the same way as in experiments with forced oscillations weight on a spring (§ 12).

If the sound is a note ( periodic oscillation), but is not a tone (harmonic vibration), then this means, as we know, that it consists of a sum of tones: the lowest (fundamental) and overtones. The tuning fork must resonate to such a sound whenever the frequency of the tuning fork coincides with the frequency of any of the harmonics of the sound. The experiment can be carried out with a simplified siren and a tuning fork, placing the hole of the tuning fork resonator against the intermittent air jet. If the frequency of the tuning fork is equal to , then, as is easy to see, it will respond to the sound of the siren not only at 300 interruptions per second (resonance to the main tone of the siren), but also at 150 interruptions - resonance to the first overtone of the siren, and at 100 interruptions - resonance on the second overtone, etc.

It is not difficult to reproduce with sound vibrations an experiment similar to the experiment with a set of pendulums (§ 16). To do this, you only need to have a set of sound resonators - tuning forks, strings, organ pipes. Obviously, the strings of a grand piano or an upright piano form just such a very extensive set oscillatory systems with different natural frequencies. If, by opening the piano and pressing the pedal, we sing a note loudly over the strings, we will hear how the instrument responds with a sound of the same pitch and similar timbre. And here our voice creates a periodic force through the air that acts on all the strings. However, only those that are in resonance with the harmonic vibrations - the fundamental and overtones that make up the note we sing - respond.

Thus, experiments with acoustic resonance can serve as excellent illustrations of the validity of the Fourier theorem.

Story

see also

  • Tuner for tuning musical instruments

Notes


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    See what “Tuning fork” is in other dictionaries: Tuning fork...

    Spelling dictionary-reference book - (from Latin camera, and tonus tone). A steel instrument in the form of a two-pronged fork, through which the tone of a singing chapel is given. Dictionary foreign words , included in the Russian language. Chudinov A.N., 1910. TUNING FORK from lat. camera, and tone, tone.… …

    Dictionary of foreign words of the Russian language Fork - Tuning fork. TUNING FORK (German Kammerton), a device (self-sounding vibrator) that produces a sound that serves as a pitch standard when tuning musical instruments for choral singing. The standard frequency of the A tone of the first octave is 440 Hz. ... Illustrated

    - (German Kammerton), a device (self-sounding vibrator) that produces a sound that serves as a pitch standard when tuning musical instruments for choral singing. The standard frequency of the A tone of the first octave is 440 Hz... Modern encyclopedia

    - (German: Kammerton) a device that is a sound source that serves as a standard for pitch when tuning musical instruments and in singing. The reference tone frequency for the first octave is 440 Hz... Big Encyclopedic Dictionary

    TUNING FORK, tuning fork, husband. (German: Kammerton) (music). A fork-shaped steel instrument that produces a sound when struck solid always the same sound, which is used as the main tone when tuning instruments in an orchestra, as well as in a choir... ... Dictionary Ushakova

    TUNING FORK, huh, husband. A metal instrument that produces a sound when struck, which is the standard of pitch when tuning instruments and in choral singing. | adj. tuning fork, oh, oh. Ozhegov's explanatory dictionary. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 … Ozhegov's Explanatory Dictionary

    - “TUMING FORK”, USSR, ODESSA film studio, 1979, color, 115 (TV) min. School movie. Ninth graders deal with their problems. Odessa version of films by D. Asanova. Drawings by Nadya Rusheva were used. Cast: Elena Shanina (see SHANINA Elena... ... Encyclopedia of Cinema

    - (diapason, Stimmgabel, tuning fork) serves to obtain a simple tone of a constant and certain pitch. This is its importance in both physics and music. It is usually prepared using steel and looks like a fork with two completely... ... Encyclopedia of Brockhaus and Efron

    fork- a, m. A device in the form of an elastic steel two-pronged fork that, when struck, produces a sound of a certain frequency, a conventional tone for tuning instruments. [I] came up with a symphony. I will introduce into it the chords of hundreds of bells, tuned to various tuning forks (V.... ... Popular dictionary of the Russian language

Books

  • Tuning fork of childhood and some masterpieces. Stories about big and small in kindergarten, Zhuravleva L.V.. This book tunes teachers and parents to that tuning fork of childhood, which allows you to feel the special beauty of life with children.

It can be partly considered methodological, revealing... Beats are a special case wave interference (see next section). The essence of the beating phenomenon is that the sum of two harmonic vibrations

close frequencies n 1 and n 2 are perceived as an oscillation with a frequency n equal to (n 1 +n 2)/2 and an amplitude that periodically changes over time with a frequency n B = |n 1 -n 2 |. mastering the method of measuring vibration frequency using the phenomenon of beats.

METHOD IDEA

For measurements using the beat method, some reference frequency, let's say n 1 . Oscillations of this frequency are superimposed on the oscillations under study. The beat frequency is directly measured, equal differences the investigated and reference frequencies n B. The desired frequency

n = n 1 ± n B. (10)

The choice of one of the signs requires additional considerations depending on the specific case.


EXPERIMENTAL SETUP

Devices and accessories: oscilloscope, two tuning forks (n 0 = 440 Hz) on resonator boxes (on one there is a scale), couplings that can be attached to the branches of the tuning fork, stopwatch, microphone, hammer.

Rice. 4.

The setup used in this work is shown in Figure 4. Microphone 1 located in the space between the resonator boxes 2 . Exactly there sound vibrations created by tuning forks 3 , have maximum amplitude. The electrical signal from the microphone is recorded by an oscilloscope 4 .

PROGRESS

1. Remove the sleeve from the graduated tuning fork. Place one of the couplings on the other tuning fork closer to the center of the branch. A tuning fork without a muff in this case is the standard one.

2. Power up the oscilloscope alternating current 220 V and let the device warm up for 2-3 minutes: a luminous dot should appear on the screen. Using the control knobs (brightness, focus, shift along “X” and “Y”) on the instrument panel, move the point to the center of the screen, achieve sufficient brightness and sharpness.

3. If you hit both tuning forks with a hammer, the luminous strip on the screen will periodically change its length due to sound beats. Set up your oscilloscope. To do this, lightly hit one of the tuning forks with a hammer and use the “Gain” switch on the oscilloscope panel to achieve a noticeable “stretch” of the luminous point on the screen in the vertical direction. Now you can take measurements.

4. Measure the time t possible with a stopwatch more n periods of "breathing" of the strip on the screen. According to the formula n B = n/t calculate the beat frequency.

5. Using the formula n 1 = n 0 - n B, calculate the frequency of the tuning fork with the sleeve attached.

6. Repeat the n 1 measurement several times and find the average value.

7. Attach the muff to a tuning fork with graduations. Now this tuning fork will be the one being studied, and the other, whose frequency n 1 has already been measured, will be the reference one.

8. Using the described method, determine the beat frequencies and natural frequencies of a tuning fork with a muff for its different positions on the tuning fork branch.

9. Plot a graph of the frequency of the tuning fork versus the distance of the muff to the base of the tuning fork. Explain the observed patterns.

TEST QUESTIONS AND TASKS FOR WORK

1. Describe the phenomenon of beats.

2. Describe the idea and features of measuring frequency using the beat method.

3. In your opinion, what are the advantages and disadvantages of this method of measuring frequency?

4. Describe experimental setup, used in work.

5. What is the function of resonator boxes?

6. Why does the frequency of the tuning fork change when you move the muff? Justify the choice of the ²-² sign in this formula 10.

7. Explain your experimental results.

8. **Two tuning forks mounted on resonator boxes have natural frequencies w 1 and w 2. When one tuning fork is excited, the second one practically does not sound. How can you make a second one sound by exciting only one tuning fork?

9. ** Let there be two tuning forks at your disposal A And B with long branches and two muffs. The task is to do the work described. As you have probably already seen, if you attach a muff to one of the tuning forks, then as the distance from the base of the tuning fork to the muff increases, the beat frequency increases, and, sooner or later, its measurement becomes impossible. However, it would seem that this could be done. First, on one tuning fork, for example, A fasten the coupling relatively close to the base of the fork and, using a tuning fork B as a standard, measure the frequency of the tuning fork A. Now the tuning fork A can be used as a reference, put the muff on the branch of the tuning fork B and determine its frequency for the position of the muff higher than on the tuning fork branch A. Again, select the tuning fork as a reference B already with the new position of the muff, and measure the frequencies of the tuning fork A for new positions of the coupling attached to it. Thus, by alternately using tuning forks as reference ones, it would seem possible to determine the frequencies of the tuning fork A for all possible positions of the muff on it. What do you think is the disadvantage of this method?



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