Acoustics

Acoustics

1. Speech Chain

   • Ling > Phys > Acoustic > Phys > Ling

2. Propagation of sound

   • Sine wave
     • Particle move & pressure variation in space
     • Pure tone
       • Basis of complex, periodic sounds

3. Sound waves

   • Frequency
     • Hz (number of cycles per second)
       • Healthy ear: 20-20,000Hz
       • Cycle (complete vibration)
         • Period = T = duration of complete cycle (s)
           • T = 1/f (s)
     • Speed of sound
       • c = 331.4*sqrt(1+Temp/273)
         • c = 340 m/s as approx value
       • Freq. does not determine speed a wave travels at
     • Wavelength (spatial period of wave)
       • λ = c / f [m]
     • Pitch
       • Freq. closely related to (but not the same as) pitch
         • Freq = physical props. of sound
         • Pitch = sensation
         • near-linear up to 1 kHz - listener's sensitivity decreases as we go higher in freq.
     • is independent of
       • Tuning fork emits the same freq. regardless of how hard it has been struck
   • Amplitude
     • dB (size of variation in air pressure)
       • peak deviation from normal atmospheric pressure
       • how forceful the wave is
         • Decibels = relative loudness of sounds in air
   • Phase
     • degrees (starting point of a wave along the y-axis)
     • Situation of the cycle of oscillation at a particular moment
     • Two Sine Waves added
       • In-phase = largest output
       • In intermediate phase = intermediate output
       • In opposite phase = zero output (silence)

4. Sound Classification

   • Periodic
     • Complex
       • >1 frequency
       • freq's which are int. multiples of lowest one = fundamental = f0 = H1
       • Power Spectrum (Amp Spectrum or Magnitude Spectrum)
     • Fourier's theorem
       • A periodic function, f(x), which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which has specific AMPLITUDE and PHASE coefficients (known as Fourier coefficients)
         • Fourier Transform
           • Discrete Fourier Transform (DFT)
             • Time-domain to Freq-domain
               • Freq-domain repres. = Hz (freq - X) vs. dB (amp - Y)
           • Fast Fourier Transform (FFT) - fast algo for DFT
           • Breaks into sine and cosine waveforms
   • Aperiodic
     • Continuous (fan, engine)
     • Transient (door closing)

5. Sound

   • Energy produced by a vibrating source which travels through the air
     • Vibration: simple harmonic motion (SHM)
       • Elasticity (bounce back)
       • Inertia (keep moving)
       • Periodic
       • Amp decreases
   • Movement of air particles -> variation in air pressure
     • Compression (high pressure)
     • Rarefaction (low pressure)
     • Longitudinal wave (pushes and pulls)