27-aug-15 physics 1 (garcia) sjsu chapter 21 musical sound

Apr 21, 2023 Physics 1 (Garcia) SJSU

Chapter 21 Musical Sound

Apr 21, 2023 Physics 1 (Garcia) SJSU

Musical InstrumentsNow that we understand more about the physics of sound, let’s analyze how it is produced by different types of musical instruments.

Apr 21, 2023 Physics 1 (Garcia) SJSU

Musical Notes

A musical note has four characteristics:

• Duration

• Loudness

• Pitch (e.g., soprano versus alto)

• Timbre or Quality (e.g, piano versus violin)

Let’s investigate the physical properties underlying these four characteristics.

Apr 21, 2023 Physics 1 (Garcia) SJSU

Duration of a Note

Duration is the amount of time from the beginning to the end of the note.

The tempo set by the composer establishes the conversion between the measure of a note (whole note, half note, etc.) and the number of milliseconds of time for that note’s duration.

Traditional metronome is a wind-up pendulum clock.

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Loudness & Amplitude

The loudness of a note is an indication of the amplitude of the sound.

DrumheadSame is true for a plucking guitar string, banging a drum, or blowing on a horn, etc.

The harder you strike a tuning fork, the larger the amplitude of the oscillation and the louder the sound made by the tuning fork.

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Pitch & Frequency

The faster the vibrations (shorter the period), the higher the pitch of the musical note produced.

There is a direct relationship between the pitch of a note and the frequency of the sound wave.

Apr 21, 2023 Physics 1 (Garcia) SJSU

Pythagoras & Music

Pythagoras discovered that different musical notes were related by mathematical ratios, such as the ratios of lengths or sizes in musical instruments or even in simple objects.

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Octave

The note produced by two strings, one half the length of the other, sounded similar.

In Western music these two notes are said to be an octave apart.

Sing “Some-where over the rainbow…”

Men and women typically sing an octave apart.

C5

C4

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Perfect Fifth

If the second string is 2/3rd the length then the

two notes are said to be “a fifth apart.”

G4

C4

Typical separation between tenor and bass or soprano and alto.

Sing “Twin-kle, twin-kle little star…”

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Fundamental & OvertonesThe Fundamental is the lowest frequency standing wave.The Overtones are twice, three times, etc., the frequency of the Fundamental.

110 Hz (A2)

220 Hz (A3)

330 Hz (E4)

One Octave

Perfect Fifth

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Notes and Powers of Two

An octave has 12 steps and going up an octave doubles the frequency.

The frequency of “Concert A” is 440 Hz.The frequency of other notes is

(Frequency) = 2(steps)/12 x (440 Hz)

counting number of steps from Concert A

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Notes & Frequencies

C (Do) C# D (Re) D# E (Mi) F (Fa)

262 Hz 277 Hz 294 Hz 311 Hz 330 Hz 349 Hz

F# G (So) G# A (La) A# B (Ti)

370 Hz 392 Hz 415 Hz 440 Hz 466 Hz 494 Hz

Middle C

Concert A

For example, Middle C is 9 steps below Concert A so it is

(Frequency) = 2(-9)/12 x (440) = 2(-0.75) x (440) = 262 Hz

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Piano Keyboard (Upper Half)

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String InstrumentsStanding wave on the vibrating string causes forced oscillation of the sounding board.

Frequency for a string depends on:• Length of string• Thickness and composition• Tension in the string

Loudness depends on:• Amplitude of oscillation• Mass of the string• Frequency

Modern piano has many long, massive steel strings under high tension (hundreds of pounds) on a large sounding board.

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Evolution of the Piano

Dulcimer

Harpsichord

Clavichord

PianoHammer

Visit the Beethoven Center on the fifth floor of MLK library.

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Musical Pipe Instruments

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Demo: Hoot TubesLarge tube has a metal screen near

one end.

Heat screen with a flame.

Remove tube from the flame and it

plays like an organ pipe.

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Hoot Tubes, Analyzed

Remove the flame and hot air rises from the screen, drawing in air from the bottom.

Hot air rising through the pipe produces pressure vibrations with a frequency determined by the pipe’s length. FLAME

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Demo: Whirly Tube

Whirl a corrugated tube to produce a pure tone at the tube’s natural frequency.

Bernoulli principle creates low pressure at the moving end, drawing air through the tube.

A

L

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Playing Simple Horns

Standing waves of different frequencies (different notes) are produced, depending on how musician blows into the horn.

Simple bugle is just a long pipe wrapped in a coil so it’s compact.

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Brass & Woodwind Vibrations

Vibrations in a pipe instrument created by:• Vibrating one’s lips (e.g., trumpet)• Blowing past an opening (e.g., flute)• Blowing & vibrating a reed (e.g., clarinet)

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Demo: Playing a Straw

Can make a simple reed by cutting a straw, as shown, lightly placing it between your lips, and blowing hard.

What happens if you shorten the straw (e.g., cut it in half)?

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Harmonic Series

Music for natural horns and bugles is limited by harmonic series, the frequencies of the fundamental and overtones.

Fundamental

Changing the Length

Finger-holes

Disadvantage: Reduced amplitude

Cornett

Crooks

Disadvantage: Clumsy

To play notes beyond the harmonic series requires changing the frequency of the fundamental by changing the length of tube.

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Changing the Length

Trombone uses a continuous slide to vary its length

Cornett

Apr 21, 2023

Changing the Length

Valves used in trumpet, tuba, and French horn

Cornett

Similar to using a crook but easy to open & close

Woodwind Instruments

Resonant standing waves also produced in a pipe but the pipe length varied by air holes (finger-holes, keys, or pads).

Flute

Clarinet

Saxophone

Oboe

Bassoon

Meter stick

Cor anglais

Using air holes reduces amplitude of the sound

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Percussion InstrumentsCreate oscillations by

striking an object, such as:

• Stretched drumhead

• Metal rod or disk

• Wooden object

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Drum Heads

Drum heads are stretched membranes that vibrate at different frequencies depending on the membrane’s oscillation pattern.

Note: These animations are not accurate because complex patterns should oscillate faster.

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Timbre or QualityA musical instrument playing a single note produces not

just that note’s frequency but others as well, mostly overtones.

The frequencies produced by a flute playing an A (slightly flat) show that the fundamental (436 Hz) and the harmonic (872 Hz) have almost the same amplitude.

The spectrum of a tuning fork would have only a single peak at the fundamental.

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Why Instruments Differ

The unique spectrum of frequencies for an instrument gives that instrument a unique signature, called the timbre (or quality). Playing this

note (196 Hz)

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Adding Different Frequencies

Two waves of different frequencies will alternate between constructive and destructive interference, as they alternate between in phase and out of phase.

Same effect seen with two combs with different tooth spacing.

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BeatsWhen the two frequencies are almost the same, the sum is about the same frequency but periodically varying amplitude. This is called a beat.

Wave A

Wave B

Sum ofA + B

In phaseOut of phase

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Dissonance & The Ear

Different tones stimulate different spots on the basilar membrane in the cochlea.

When two tones are close together, the stimulation of two nearby spots is unpleasant and heard as dissonant.

Cochlea “unrolled”