# Acoustics

• Sound is the perception of vibration of our eardrums.
• The Minim package is a user-contributed audio library in the processing library for playing, manipulating, and synthesizing sound.
• A musical note is a wave that oscillates at a certain frequency.
• We will use concert A, the A above middle C, as a reference note.
• Concert A (also known as A440, A4, Stuttgart pitch) has been standardized to oscillate at a frequency of 440 times per second (Hz).
• When you double or halve the frequency, you move up or down one octave on the scale. E.g., 880 Hz is one octave above concert A; 110 Hz is three octaves below concert A.

# Acoustics, continued

• A newborn baby can hear sound waves of frequency between 20 to 20,000 Hz. People lose the ability to hear the high-frequency sounds as they grow older.
• The sin function repeats itself once every $$2\pi$$ units, so if we measure $$t$$ in seconds and plot $$\sin(2\pi t \times 440)$$, we get a curve that oscillates 440 times per second.
• The amplitude of the wave determines what we perceive as volume. We'll plot our curves between –1.0 and +1.0 and assume the devices that record and play sound will scale as appropriate.
• When a guitar string is plugged, the string vibrates, producing a sine wave that is the prominent part of the sound that you hear and recognize as a note.
• There are 12 notes on the chromatic scale, evenly spaced on a (base 2) logarithmic scale. For any given note, we get the $$i$$th note above it by multiplying its frequency by $$2^{i/12}$$.

# Chromatic scale

note i frequency
A 0 440.00
A♯ or B♭ 1 466.16
B 2 493.88
C 3 523.25
C♯ or D♭ 4 554.37
D 5 587.33
D♯ or E♭ 6 622.25
E 7 659.26
F 8 698.46
F♯ or G♭ 9 739.99
G 10 783.99
G♯ or A♭ 11 830.61
A 12 880.00

# Sampling

• For digital sound, we represent a curve by sampling it at regular intervals.
• We will use the commonly used sampling rate of 44,100 samples per second.
• For concert A, that rate corresponds to plotting each cycle of the sine wave by sampling it at about 100 points.
• We represent sound as an array of real numbers between –1.0 and +1.0.