Definition of Sound Sound Psychologist's = that which is heard Physicist's = a propagated disturbance in the density of an elastic medium Vibrator serves as the sound source Medium = air 2 Vibration Periodic = repetitive Simple Physical = Sinusoid (uniform circular motion) Psychological = Pure tone Complex 2 sinusoids with different frequency Aperiodic = not repetitive Transient = clicks Noise = random vibrations Period - Frequency Time to complete full cycle = Period = "T" # cycles completed in sec = Frequency Old units = cps; d.v. Current = Hz (named for Heinrich Hertz) Reciprocal relation T = sec/cycle F = cycle/sec F = l/t, and vice versa 3 4 Parameters Any sinusoid can be completely described by 3 parameters: frequency (period) amplitude phase Amplitude Waveform Plot of amplitude as a function of time T = ms F = 000 Hz 0 0.25 0.5 0.75 5 Time (msec) 6
Amplitude Waveform Plot of amplitude as a function of phase angle.5 0.5-0.5 Sine Cosine 0 0 45 90 35 80 225 270 35 360 Superposition Waveform of combined sinusoids = algebraic sum of the component waveforms - -.5 Phase angle (degrees) 7 8 Combining Sinusoids of the Same Frequency Combining Sinusoids of Different Frequency 9 0 Complex Waves Definition = any periodic waveform composed of 2 or more sinusoids with different frequencies Waveform shape is completely and uniquely determined by: Frequency and amplitude of component sinusoids Phase relation among components (less important) Fourier Analysis Mathematical technique to break down complex waveforms into simple component parts Enables analysis of the most complex of waveforms 2 2
Spectrum Time vs. Frequency Domain Spectra (pl.) In the frequency domain, vibrations are specified by their spectrum: Amplitude spectrum Plot of amplitude as a function of frequency Phase spectrum Plot of starting phase as a function of frequency Line Spectrum Characteristic of all periodic waveforms 3 4 Spectrum Harmonic Structure All components in a periodic wave MUST be integral multiples of its repetition rate N x (rep. rate), where N = an integer N = = first harmonic = fundamental frequency N = 2 = second harmonic = first overtone Etc. Environmental Sounds Sinusoids = rare Complex waves = common (e.g., vowels, music) Noise & transients = very common 5 6 Sound Waves Longitudinal waves Particles move in same direction as wave is transmitted Types Spherical Source = small point, or a sphere Plane Source is a large, flat surface Environmental sounds are combination Sound in the Real World Sound at any point = the combined effects of sound wave emanating directly from the source and reflections (or echos) 7 8 3
Pressure Sound Magnitude Force per unit area Units Old cgs system dynes/cm 2 dyne = move gm, cm in sec aka microbar (µbar) Le Systeme International (SI, or MKS) newton/m 2 aka pascals (Pa) -- Blaise Pascal Preferred term 9 20 Problem Dynamic range of hearing is extreme Faintest audible sound 20 µpa Loudest tolerable sound 200,000,000 µpa Ratio of ten-million to one! The db is: A ratio Between any 2 numbers Dimensionless Standard reference values must be specified A logarithmic measure Addition of logs = multiplication of original numbers To add and subtract the original values convert from db's to original pressure or power units perform the + or - operation re-convert the result to db's 2 22 Solution Use logarithms to specify sound magnitude Specifically Form a ratio between the sound level of interest and a standard reference level Take the logarithm of that ratio: Log (sound level/reference level) Units = Bel Decibel = /0 Bel = db Intensity Level (IL) Useful for measuring environmental sound since the combined effect of multiple sound sources results from the addition of their intensities. Standard reference value 0-2 Watts/m 2 (mks) 0-6 Watts/cm 2 (cgs) 23 24 4
Sound Pressure Level (SPL) Hearing Most useful re: hearing because pressure is what moves your eardrum. Standard reference value: 20 µpa (mks) 0.0002 dyne/cm 2 (cgs) Physical Amplitude Frequency Time Psychological Loudness Pitch Duration 25 26 5