Physics Midterm 1

Sound Waves

longitudinal waves

flicker fusion rate - lowest we can process is ~20/sec

waveform = combo of repeated waves

amplitude - controls vol lvl

frequency - controls pitch, measured in cycles/sec or Hz

shape - controls timbre/quality

just temperament vs. equal temperament

aperiodic waves are random (aka white noise)

octaves

speed of sound = 343 m/s (or 1 mi/4.7s)

depends only on temp, pressure, and gas composition

inversely proportional to length (1/length, i.e. half the length => twice the frequency)

half-steps/semitones frequency ratio = 2^1/12

physics 288-LO3 for math review

1 musical cent = 1/100th of a half-step, frequency ratio = 2^(1/1200)

almost everyone can hear change of 25 cents, few ppl can hear change of 5 cents

equal temperament

just temperament: frequency of note changes based on what key it's being played in

1 octave up = double the frequency

octave 2: C2-C3 (lower notes)

octave 3: C3-C4 (to middle C)

octave 4: C4-C5: (middle to high C)

octave 5: C5-C6

octave 6: >C6

middle C = 260 Hz

A4 = 440 Hz

Musical Notation

be able to identify types of notes and rests

fifth frequency ratio = 3/2 (1.5)

proportional to velocity (air molecules have to move faster with larger amplitudes)

Energy is proportional to amplitude squared (i.e. multiply amplitude by 2 => multiply energy by 4) E = k^2A^2

proportional to velocity

Energy is proportional to frequency squared E = b^2f^2

Energy

AMOUNT of E = joules

RATE of E = joules/s

INTENSITY = w/m^2 (watts per square meter)

amt reaching eardrum depends on eardrum size

measures how loud a sound is

proportional to A^2 and f^2

very loud = 1 W/m^2 (sound of jet airliner)

for reference: loud rock concert = 0.1, pin drop = 10^-12

Sound Intensity Level (SIL, aka sound lvl) - vol increases by certain amt every time you multiply intensity of certain amt

intensity increases by factor of 10 => SIL increases by 1 bel (2 bels = factor of 100, 3 bels = factor of 1000)

bel is a large unit, decibel more commonly used: 1 decibel = 1/10th of a bel THEREFORE 10 decibel increase in SIL = intensity increases by factor of 10

fix scale: 0 dB = 10^-12 W/m^2 (inaudible lvl)

double distance => divide intensity by 4, i.e. inverse-square law or intensity is proportional to 1/r^2

perceived loudness: measured in sones, 1 sone = perceived loudness of 1 kHz sine wave at 40 dB

loudness doubles when SIL increases by 10 dB

also affected by pitch (thus frequency) --> lower frequency sounds carry less E, ear sensitivity to certain frequencies may make some sounds seem louder

basic range of hearing = 20 Hz-20,000 Hz or 20 kHz