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Mechanism of sound creation with musical instruments

Source: licencja: CC 0.

Mechanizm wytwarzania dźwięku w instrumentach muzycznych

Instrumenty dęte (piszczałki)

You will learn
  • the rules related to making sounds with musical instruments,

  • to determine the frequency of sounds created with musical instruments in English.

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nagranie abstraktu

Answer the introductory questions.

  1. What is the wave interference?

  2. What conditions must be met to create a standing wavestanding wavestanding wave?

  3. What are the nodes and the antinodes of a standing wave?

  4. What are the harmonic waves of a standing wave?

Please, prepare the answers to the following questions.

1. What is a musical instrumentmusical instrumentmusical instrument?
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nagranie abstraktu

musical instrumentmusical instrumentmusical instrument is any object that produces sound, and this sound is used to create music.

2. What can be the source of sound in musical instruments?
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nagranie abstraktu

Because the vibrating bodies are the source of sounds, the essential element of every musical instrument must be the body that vibrates with the right frequency. This body can be a stringstringstring in stringed instruments or a column of air in brass instrumentsbrass instrumentsbrass instruments, a membrane of loudspeaker or drum, a resilient piece of metal in music boxes or cymbals, etc.

3. Classify musical instruments according to the way the sound is created.
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nagranie abstraktu

Various classifications and systematics of musical instruments are introduced in science. In this lesson, we limit the description to two popular types of instruments, i.e. stringstringstring and brass instrumentsbrass instrumentsbrass instruments.

The standing wavestanding wavestanding wave can be created in vibrating strings as well as an air column (so‑called pipes).

The following types of fifes can be distinguished:

  • open on both ends,

  • closed on both ends,

  • closed on one ends,

4. Present standing waves which are created in stringed instruments.
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Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

If a string of, e.g. guitar, is the source of the sound, then the instrument is a stringed instrument.

In places where the stringstringstring is attached, the nodes of the wave are formed.

Possible sample shapes of standing waves in a tight string with length L.

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Possible sample shapes
Source: GroMar, licencja: CC BY 3.0.
5. What is the fundamental frequency of a vibrating string, rigidly attached on both ends?
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nagranie abstraktu

The length of the transverse wave on the stringstringstring is not equal to the length of the sound wave due to the differences in the propagation velocities of both waves in both media.

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The length of the transverse wave on the string
6. Present in the graphs the share of individual harmonic components in creating the timbre of the sound.
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Source: GroMar, licencja: CC BY 3.0.
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Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

When a vibrating column of air is the source of sound, then we talk about fifes. Depending on the construction of the instrument, fifes can be closed on both ends, open on both ends or semi‑open.

In the place when the fifefifefife is closed, the nodes of the standing wavestanding wavestanding wave are formed, while their antinodes appear at the open ends.

Frequency of vibrations of air column in fifes

7. Present the standing waves which occur in the fife which is open on both ends.

The fifefifefife is open on both ends.

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The fife is open on both ends
Source: GroMar, licencja: CC BY 3.0.
8. What is the fundamental frequency of a vibrating air column in the fifefifefife open at both ends?
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nagranie abstraktu

The situation is analogous to that of a tight stringstringstring attached on both ends.

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Source: GroMar, licencja: CC BY 3.0.
9. Present the standing waves created in the fifefifefife closed at both ends.

The fife is closed at both ends.

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The fife is closed at both ends
Source: GroMar, licencja: CC BY 3.0.
10. What is the fundamental frequency of a vibrating air column in a fife closed at both ends?
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nagranie abstraktu

The situation is analogous to that of a tight string attached at both ends.

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Source: GroMar, licencja: CC BY 3.0.
11. Present the standing waves created in the fifefifefife closed at one end.

Fife closed at one end.

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The fife closed at one end
Source: GroMar, licencja: CC BY 3.0.
12. What is the fundamental frequency of a vibrating air column in the fifefifefife closed at one end?

Vibration frequency in this case.

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Source: GroMar, licencja: CC BY 3.0.

Click on the selected instrument and its name will appear.

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Na ilustracji interaktywnej przedstawione są instrumenty muzyczne oznaczone numerami: 1 - perkusja, 2 - gitara akustyczna, 3 - saksofon, 4 - flet, 5 - trąbka, 6 - harmonijka ustna. Na ilustracji widoczne są numery, a na nich podpisy. 1. percussion {audio}, 2. guitar {audio}, 3. saxophone {audio}, 4. flute {audio}, 5. trombone {audio}, 6. mouth-organ {audio}.
Instruments
Source: GroMar, licencja: CC BY 3.0.
Summary
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nagranie abstraktu

The vibrating body such as a stringstringstring, an air column, a membrane, etc. is the basic element of every musical instrumentmusical instrumentmusical instrument. They create standing waves, which are the result of superposition of waves which move in opposite directions and consist of:

  • nodes - places where the particles of the medium do not vibrate,

  • antinodes - places where the amplitude of vibration of the medium particles is maximal.

The distance between two neighbouring nodes is equal to half the wavelength running in the medium.

The pitch (frequency) of the sound emitted by the instrument depends on the longest (basic) wave that can be created in a vibrating element and is related to the size of this element.

In brass instrumentsbrass instrumentsbrass instruments the longer pipe corresponds to the lower basic frequency, and thus the lower sound.

In stringed instruments, the pitch of the sound depends on:

  • stringstringstring length, longer length - lower sound,

  • string thickness, thinner string - higher sound,

  • string tensile, greater tensile force - higher sound.

Exercises

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Exercise 1
Exercise 2

The guitar has six strings. If we do not press them at any fret, they will produce the following sounds respectively:

1

2

3

4

5

6

E (82,6 Hz)

A (110 Hz)

D (146,7 Hz)

G (195,6 Hz)

H (246,9 Hz)

E (330 Hz)

Will it cause any vibration on the other strings, if we play the empty string A? If so, which ones? Linit your vibration analysis to the first 4 harmonics.

Exercise 3

The stringstringstring A of the guitar (the second one), oscillating freely (not pressed on any fret), produces A sound with the frequency of 110 Hz.

What will be the frequency of the created sound, if we press the string on the 12th fret, at the same time the string is shortened to the half of its original length? What would you have to do with the guitar string to get the same effect without shortening the string?

Write a short answer to the above question in English.

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Exercise 4
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. instrument muzyczny - musical instrument, 2. struna - string, 3. piszczałka - fife, 4. piszczałka obustronnie zamknięta - fife closed on both side, 5. piszczałka obustronnie otwarta - fife closed on one side, 6. węzeł - antinode
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

antinode
antinode

strzałka

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wymowa w języku angielskim: antinode
brass instruments
brass instruments

instrumenty dęte

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wymowa w języku angielskim: brass instruments
fife
fife

piszczałka

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wymowa w języku angielskim: fife
fife closed on both side
fife closed on both side

piszczałka obustronnie zamknięta

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wymowa w języku angielskim: fife closed on both side
fife closed on one side
fife closed on one side

piszczałka jednostronnie zamknięta

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wymowa w języku angielskim: fife closed on one side
fife opened on both side
fife opened on both side

piszczałka obustronnie otwarta

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wymowa w języku angielskim: fife opened on both side
musical instrument
musical instrument

instrument muzyczny

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wymowa w języku angielskim: musical instrument
node
node

węzeł

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wymowa w języku angielskim: node
standing wave
standing wave

fala stojąca

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wymowa w języku angielskim: standing wave
string
string

struna

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wymowa w języku angielskim: string

Keywords

fifefifefife

musical instrumentmusical instrumentmusical instrument

nodenodenode

standing wavestanding wavestanding wave

stringstringstring

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