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acoustic wavform in brass instrument if a closed tube

author:MF manufacturerstime:2022-03-13 21:15:26

1. Wooden tube sound

The sound of the vole instrument is mainly based on the incentive of the hand blowing.(frequency),Resist an adjustment frequency with the resonance of the body and air column、Tone。There are two main types of motivation:

  1. Cutting air incentive。Such as flute、Flute,It relies on adjustment blow angle,Cut the air blown air“Edge prism”,The edged edge is mainly after the airflow is cut.,Generated reflow causes constant changes in air pressure,The back-and-round movement caused by the air pressure difference produced a foundation noise(energy),In detail。The twin is directly placed in the whistle to cut,Blowing the port and the direction of it is,Directly blow it,And flute can adjust the angle of blowing yourself。In order to get special resonance and excitation,Some wood tubes also have a film。
  2. Vibrating reed,Divided into a single spring and a double spring。Such as a clarinet,Twians,It is a reed to return to the air pressure change of the control of the airflow.,To provide basic energy(frequency)。The frequency of the reed-retracted closure is affected by the vibration frequency of the reed itself.,At the same time, the vibration of the reed will also produce a sound.,Pipe is responsible for coupling adjustment of overall tone and pitch。Due to the participation of the reed,Its sound and the wood tube that rely on cutting air have a lot of difference.,I can distinguish it when I hear it.。

There are two main types of pipes.:

(acoustic wavform in brass instrument if a closed tube)1. Opening tube,Refers to the tube that is not closed at both ends。Such as Changli bamboo flute。

(acoustic wavform in brass instrument if a closed tube)2. Closed tube。Refers to a separate one-end closed tube。For example, one end is a reed tube、One end is a clarinet of the open mouth,Double archipe,Or whistle end is not closed,Another section is a whistle that the sliding device is plugged in the lower end to adjust the tall。

Next, tell the difference。

Let's talk about the two vibration modes of the pipe。

2. Wooden tube standing(Resonance)Model

(acoustic wavform in brass instrument if a closed tube)2.1 Opening tube

we know,The spread of acoustic waves is a change in media pressure,We observe the sound pressure during acoustic wave communication,Media(Air)Exist“Be compressed-Become thin-Be compressed-Become thin”This continuous reciprocating action,Spend forward。We takexAxis time,byyAxis is sound pressure,Sitting in a fixed position to observe the changes in sound pressure,Can draw waveforms,The wave festival is a pressure balance point(Atmospheric pressure),And the upper raft is the most compressed one,The lower abdomen is the most sparse。

acoustic wavform in brass instrument if a closed tube

Painless,Take a look。

Both ends are a standing wave propagation within the open end(The standing wave can be understood here as a waveform that can continue in the tube.,Detailed Interpretation See the link to explain the tone),belongBoundary area(Inside the pipe)Infrared area(Outside)Spread,Sound pressure is reflected in the tube。In the boundless area to the boundless area(Open end)Generated reflection,Opener and atmosphere Unicom,It means that the opening is inevitably atmospheric pressure,This means,Positive direction sound pressure+Final synthetic waveform after reflecting sound pressure,The opening end is inevitable to be sound strong(Sound strong wave section is equal to atmospheric pressure)!!!if not,Then it's notCannot be enhanced and continuous,MaybeSubtilize、dissipate,In other words,Only when the waveform is in line with both ends, it is a sound pressure wave.,This waveform can continue to exist in the opening tube.。Then we can list the frequency at both ends in countless sound pressure wavefronts.,Hypothesis2,As shown below(Only list,Hypothesis2):

acoustic wavform in brass instrument if a closed tube

Then we can find the law:Panfer is all multiples of the fundamental frequency。

The formula is as follows:


acoustic wavform in brass instrument if a closed tube(acoustic wavform in brass instrument if a closed tube)

in,LRefers to the tube length of both ends,

λWavelength wavelength。Change formula according to frequency and wavelength:λ=V/f(inVSound speed),Easily get the frequency。

The next detailed explanation why only these frequencies can exist。

(acoustic wavform in brass instrument if a closed tube)Remember a law first:In this reflection bound to the boundless area,The most demise reflection of the sound pressure becomes the spare point of sound pressure,The most sparse-point reflection becomes the most secret。

From waveform,Suppose there is a waveform from left to right,According to the law,existx=5Anti-reflection,The waveform after the reflection isx=5Right waveform inverse,In one anotherx=5Turn over the symmetry。

(acoustic wavform in brass instrument if a closed tube)The minimum frequency that we can generate with pipes——Base frequency as an example,The picture below is different time points.,For the inner direction of the pipe、Reflection sound and strengthen“Photo”:

acoustic wavform in brass instrument if a closed tube

(This picture made me all day.↑…Ask if there is any convenient software for this mathematics.,psThe warrior is exhausted。。

(acoustic wavform in brass instrument if a closed tube)Through observation and argumentation,The production of the base frequency is fully compliant with the above law,Other multiples are also the same。At the same time,Reflective sound pressure More than this bunch,There is also a second reflection waveform after reflection of reflection.,But you will know,Stating wave frequency,The secondary reflection waveform is the same as the incident waveform.,Concrete,Three reflex waveforms and one reflection waveform。The standing wave is like this,Enhanced can be continued in the tube,And other waveforms that do not meet the standing wave frequency,Not enhanced。

(acoustic wavform in brass instrument if a closed tube)For the excitation end that causes gas prism,This end is constantly transporting the sound pressure generated by gas in the tube.,And this paragraph and atmosphere Unicom,soOne end of the whistle that causes gas prisms by cutting air belongs to the opening end

The gas can be sent out.,Bite your lipssssssthe sound of,It is a tone.。This sound isNo noise in fixed frequency,And it has a minimum frequency f0,existf0The following frequency band is not energy,Noise is only distributedf0above。at the same time,f0The pitch formula is as follows:

acoustic wavform in brass instrument if a closed tube

in,vAir supply,LRefers to the diameter of the opening,That image8The symbol is positive correlation。Blowing wind speed relying on mouth adjustment,The faster the air flow rate,His base frequency is higher;If the blow is opened, the greater,The lower the pitch。This formula is used to the super blow.,Let's talk about it。

Pneumatic,The entire wood tube itself will be used asAtronize tube,Tube length and structural coupling、Adjust the pneumatic sound,So what you have heard is not a simple noise,But the sound after the tube is modified.。

2.2 Closed tube(Cylindrical closed tube)

(acoustic wavform in brass instrument if a closed tube)Closed tube,That is, one end is open,One end is an unopened pipe,Do not generate a wave of flood belly at both ends。There is a case:

  1. One end is the whistle(Open end),Another section is a closed movable device to slide adjustment sound
(acoustic wavform in brass instrument if a closed tube)acoustic wavform in brass instrument if a closed tube

This can also be sold200many??????cost1Yuan is not good.???????IQ???

(acoustic wavform in brass instrument if a closed tube)The activity device under the bottom is a steel structure,The sound wave encounters the reflection of this hard structure and encounters the wall reflection.。Special,Only the whistle is open,The other section is a steel closure end。There is a law here:Reflection of sound waves on the steel interface,The most dense reflection of the sound pressure is also the most secret,The most sparsely reflected is still the most sparse。

From waveform,Set up a waveform from left to right,existx=2.5In accordance with the above regular reflection,The waveform after the reflection isx=2.5On the right waveformx=2.5Directly over the symmetry shaft。

Since the opening end of the atmosphere is necessary to be a wave section,And one end of the rigid interface can be any point in the phase,Further, according to the above reflection law,We can learn,Closed tube is like a stationary wave,The standing wave is inevitably a wave section,The abdomen of the standing wave is in the closed end(If the tube is not satisfied1/4Odd number of waveforms,Reflective sounds will have a variety of offset after the open end is reflected again.,It is possible to cancel again after being reflected by the closed end.,The sound cannot be continuous;If,The secondary reflection sound after the opening of the open end is just equal to the incident sound.,Each waveform strengthens each other,Form a standing wave)。We can draw all waveforms that can continue in the closure tube:

Only list some(Hypothesis2.5):

acoustic wavform in brass instrument if a closed tube

Formula:

acoustic wavform in brass instrument if a closed tube

Identify the resulting frequency only base frequency+Wonderful harmonics(Or even preference)。

We can useFormula demonstrationWhy not even harmonic:

Assume a closed tube,One of them has an incident soundf(x),The length of the closed tube is equal tof(x)Wavelength1/2Intensity,Set the tube lengthL,With the opening end,Build a right angle coordinate system。

f(x)Have a hard interface(x=L)The first reflection sound isg(x),According to the principle of reflection,g(x)andf(x)The relationship is symmetrical in hard borders,sog(x) = f(-x-2L);g(x)Enabled open border,Secondary reflection sound generated after reflectionh(x)andg(x)The relationship is symmetrical with open borders and inverse,geth(x)=-g(-x),soh(x)=-g(-x)=-f(x+2L);In -f(x+2L) middle,2LWait equal to one or more complete cycles,so-f(x+2L) = -f(x),The second reflection sound is inversely opposed to the incident sound,Two additions:h(x)+f(x)=f(x)-f(x)=0,Directly offset,No room for spread。

ifLNot a wavelength1/2Intensity,Why1/4Odd times,So2LApproach is equal to the wavelength of half a cycle,At this moment-f(x+2L)andf(x)Phase,Completely coincide,Overlay。The same is true of other reflection waves。

(acoustic wavform in brass instrument if a closed tube)According to formula+We can still learn about the waveform,Same,The baseband of the closed tube is lower than the open tube8Spend(Two times)。

We can be based on the above law,Draw a positive direction on each time、Reflective sound waves and synthetic acoustic waves“Photo”(As previously shown)~

2. One end is a reed(Closed end),Another open instrument,Such as a double spring tube。(Cylindrical)

Why is the reed end belong to a closed end?Let's first understand the role of reeds.:

Reprollement,Causing a vent“open-combine”Action constant reciprocation,Thus, enter the sound,provide energy。The reed is closed when closed,This end is not working with the atmosphere,Closed end;The energy of the spring can be raised to a certain level,When starting open,Instantly enter a sound inquate,Post-instant closed,Blocked the atmosphere,The improvement of the energy is once again promoted,Closed again,Such a reciprocation;Or the reed only leaves a slit that is much smaller than the pipe diameter,This gap has little effect on air vibration in the pipe.,This end is equivalent to a hard interface。

(acoustic wavform in brass instrument if a closed tube)This type of vibration mode and the above“One end of the whistle is closed”The vibration mode is exactly the same,Only open the open end in your ass,Closed end in mouth。

For reeds,Its vibration frequency is the frequency of free vibration of the tube,Soft reed(Such as reed tablets)Can be easily coupled to body,The sound of the actual situation of the reed is also the sound after the frequency of the tube is coupled.。Due to the participation of the reed,The sound of the spring instrument and the sound of the reed instrument has their own distinctive features。

(acoustic wavform in brass instrument if a closed tube)Cylindrical closed tube's preference only,Because people can only send a wonderful harmonics。

(acoustic wavform in brass instrument if a closed tube)3. Conical instrument(Also closed tube)

Such as double spring tube。For musical instruments close to cone type,It can make a wonderful harmonics and even harmonics。Because one end of the pipe diameter is extremely small than the other end,The waveform after the reflection of the open end is affected by it.,Ball speed decrease,Almost no reflection occurred。Above we argue,One end closed tube,The secondary reflection wave of the occasional harmonics offsets with the original waveform,So only odd times can be left。And conical,Secondary reflection waves are blocked,There is no case where the secondary reflection wave is unsearched with the original waveform.,Reflection only exists。So it can issue all integer harmonics。

If the opening inner diameter of the closed diameter pipe is not completely unified,Also biased toward a little conical,Then it will make it bring some of the characteristics of cone tubes.(Bring a little harmonic)。

3. Wood tube

The source of sound in the wood tube is supplied by the whistle or reed.,fingering(Conversion tube)And the energy from the mouth will affect the sound。There are two main principles of super blowing::

  1. Vibration mode blocked
(acoustic wavform in brass instrument if a closed tube)I can only play the recorder,So I take the most familiar recorder as an example。

clarinet fingering chart:

(acoustic wavform in brass instrument if a closed tube)acoustic wavform in brass instrument if a closed tube(acoustic wavform in brass instrument if a closed tube)

There is a treble hole in the back of the recorder,for thumb,by opening/half open/Close this hole for a higher tone,The other seven holes in front of it are used to adjust the reference pitch.。

Observe carefully,Some sounds can be found(for example3、4、5、6)in small print1group and small print2group on,Front7Fingering is the same,The only difference is whether the thumb hole is closed or half-open,Why is it possible to control the high and low octaves only through the treble hole??

The hole of the treble hole is exquisite,It must be played at the antinode position of the first harmonic of certain pitches of the flute body。we know,The recorder is a double open mouth tube,Both ends are sound pressure nodes,The lowest frequency is the fundamental,Then if I make a hole at the antinode of the lowest sound pressure,Then this point is connected to the atmosphere,must be knots,Then the frequencies that are antinodes at this point will be“air leak”,can be easily suppressed,can't send。at this time,The lowest frequency that can be emitted is exactly the second harmonic of this frequency(one overtone),Because this harmonic is just a node at this point,does not affect,At the same time, all multipliers of this frequency are also nodes at this position.,does not affect,So the vibration of the whole canal entersSecond harmonic mode。This is by hitting“tweeter hole”to control the principle of high and low octaves。

3、4、5、6The fundamental frequency antinode of the tone is just near the treble hole(It can be easily obtained by calculating the tube length),So it can be suppressed in this way,Get an octave higher;And the antinodes of other parts are not exactly in this position,You can't get a higher octave this way,So it's not universal。

For cylindrical tubes closed at one end,Its standing wave mode has no second harmonic,Only odd harmonics are present,So the blow out is not high8degree of sound,rather high15degree of sound(see overtone column),Vibration comes in3rd harmonic mode。

Because the conical tube can emit strange/even overtones,All modes are possible。

(acoustic wavform in brass instrument if a closed tube)recorder“Advanced blowing”,Press all the way and plug the bottom vent hole,It becomes a closed tube,The superblowing enters the third harmonic mode,higher sound。

(acoustic wavform in brass instrument if a closed tube)The clarinet, a pure natural cylindrical closed tube, is a third harmonic mode.(even higher)。

(acoustic wavform in brass instrument if a closed tube)2. Change the fundamental frequency of air ridgesf0

Above we talked about the air ridge tone formula:

acoustic wavform in brass instrument if a closed tube

in,vwind speed,LRefers to opening diameter。The fundamental frequency of air ridges is proportional to the blowing speed,Inversely proportional to opening size。The opening size refers to the blowing cross section,Like a flute, the blowing angle can be adjusted、Air velocity to stabilize overblown pitch,control at the same timevandL。

The recorder is a fixed whistle,Unable to adjust the blowing angle,Only the blowing speed can be adjusted。Anyone who has played the clarinet should understand,In different zones, you must use the breath of different speeds to play,Otherwise the sound will be inaccurate。Wait until the airflow is fast enough,f0high to a certain extent,The resonance tube excites the second harmonic mode,Bass fundamental cannot be excited or is weaker than the second harmonic,you can blow out a high octave,even high12degree of sound(recorder above treble7sounds like this),or higher pitch。

3. Change the reed vibration mode

(acoustic wavform in brass instrument if a closed tube)For reed instruments,Increasing the air flow rate allows the reed itself to enter a higher vibration mode,After the reed enters a higher vibration mode,The frequency of the input sound pressure also increases,The sound produced by coupling also becomes higher。

Not only that,The vibration mode of the reed can also be controlled through the lips and the reed(reed)Contact location、strength to achieve。(For example, the traditional art of blowing leaves,airflow、The pressure position of the lips on the leaves、The adjustment of the intensity can blow different pitches)

Using super blowing technology,You can widen the range of the woodwind to get more pitch。

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