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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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…”
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Piano Keyboard (Upper Half)
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
Evolution of the Piano
Dulcimer
Harpsichord
Clavichord
PianoHammer
Visit the Beethoven Center on the fifth floor of MLK library.
Apr 21, 2023 Physics 1 (Garcia) SJSU
Musical Pipe Instruments
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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)
Apr 21, 2023 Physics 1 (Garcia) SJSU
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)?
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Percussion InstrumentsCreate oscillations by
striking an object, such as:
• Stretched drumhead
• Metal rod or disk
• Wooden object
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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)
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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”