27-Aug-15 Physics 1 (Garcia) SJSU Chapter 21 Musical Sound

27-Aug-15 Physics 1 (Garcia) SJSU Musical Instruments Now that we understand more about the physics of sound, let’s analyze how it is produced by different types of musical instruments.

27-Aug-15 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.

27-Aug-15 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.

27-Aug-15 Physics 1 (Garcia) SJSU Loudness & Amplitude The loudness of a note is an indication of the amplitude of the sound. Drumhead Same 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.

27-Aug-15 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.

27-Aug-15 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.

27-Aug-15 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. C5C4C5C4

27-Aug-15 Physics 1 (Garcia) SJSU Perfect Fifth If the second string is 2 / 3 rd the length then the two notes are said to be “a fifth apart.” G4C4G4C4 Typical separation between tenor and bass or soprano and alto. Sing “Twin-kle, twin-kle little star…”

27-Aug-15 Physics 1 (Garcia) SJSU Fundamental & Overtones The Fundamental is the lowest frequency standing wave. The Overtones are twice, three times, etc., the frequency of the Fundamental. 110 Hz (A 2 ) 220 Hz (A 3 ) 330 Hz (E 4 ) One Octave Perfect Fifth

27-Aug-15 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

27-Aug-15 Physics 1 (Garcia) SJSU Notes & Frequencies C (Do)C#D (Re)D#E (Mi)F (Fa) 262 Hz277 Hz294 Hz311 Hz330 Hz349 Hz F#G (So)G#A (La)A#B (Ti) 370 Hz392 Hz415 Hz440 Hz466 Hz494 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

27-Aug-15 Physics 1 (Garcia) SJSU Piano Keyboard (Upper Half)

27-Aug-15 Physics 1 (Garcia) SJSU String Instruments Standing 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.

27-Aug-15 Physics 1 (Garcia) SJSU Evolution of the Piano Dulcimer Harpsichord Clavichord Piano Hammer Visit the Beethoven Center on the fifth floor of MLK library.

27-Aug-15 Physics 1 (Garcia) SJSU Musical Pipe Instruments

27-Aug-15 Physics 1 (Garcia) SJSU Demo: Hoot Tubes Large 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.

27-Aug-15 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

27-Aug-15 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

27-Aug-15 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.

27-Aug-15 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)

27-Aug-15 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)?

27-Aug-15 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.

27-Aug-15 Physics 1 (Garcia) SJSU Changing the Length Trombone uses a continuous slide to vary its length Cornett

27-Aug-15 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

27-Aug-15 Physics 1 (Garcia) SJSU Percussion Instruments Create oscillations by striking an object, such as: Stretched drumhead Metal rod or disk Wooden object

27-Aug-15 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.

27-Aug-15 Physics 1 (Garcia) SJSU Timbre or Quality A 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.

27-Aug-15 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)

27-Aug-15 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 Beats When 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 of A + B In phase Out of phase

27-Aug-15 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”