Acoustics exam 2

  1. What is a complex wave?
    any sound wave that is not sinusoidal
  2. What is Fourier's Theorem?
    complex waves consist of a series of simple sinusoids that can differ in amplitude, frequency, and phase (called Fourier series)
  3. How can a Fourier series be derived?
    Fourier Analysis
  4. What is Fourier Analysis?
    any complex wave can be decomposed to determine the amplitudes, frequencies, and phases of the sinusoidal components
  5. How are sound waves classifed?
    • periodicity
    • complexity
  6. What is a periodic wave?
    • a wave that repeats itself over time
    • also called a periodic time function
    • a sine wave is always periodic
    • *pg 67 slide 5
  7. Components of a complex periodic wave
    • sinusoidal components cannot be selected at random- they must satisfy an harmonic relation
    • with an harmonic relation, each sinusoid in the series must be an integer multiple of the lowest in the series
    • example: lowest = 215 Hz, components = 215, 430, 645, 860, etc
  8. Harmonic series
    • if harmonic relation is present, the series of components is called an harmonic series
    • each of the components is called an harmonic
    • *pg 68 slide 7
  9. T = 8 ms; fundamental frequency = 125 Hz. What are the frequencies of the first five harmonics?
    • 1st (fundamental) = 125 Hz
    • 2nd = 250
    • 3rd = 375
    • 4th = 500
    • 5th = 625
  10. What are the characteristics of a simple wave?
    • pure tone
    • sine wave
    • one frequency
  11. What are the characteristics of complex waves?
    • 2 or more pure tones of different frequency, amplitude, and phase added together
    • most sounds are complex
  12. What are harmonics?
    • whole number multiples of fundamental frequency
    • energy is expected but not required at each harmonic
    • in theory, no limit to number of harmonics though effect of higher frequencies is not noticeable
  13. *Summation of sine waves pg 68 and 69
  14. What are aperiodic waves?
    • waves that lack periodicity (book dropping, static)
    • noisy, turbulent sounds (fricatives)
    • pathologic voices
    • you can't get fundamental frequency and harmonics
    • *complex waves can be periodic or aperiodic
  15. What are continuous aperiodic waves?
    • more than 1 frequency
    • no harmonic relationship
    • continuous in time
    • "shhhhh"
  16. What are transient aperiodic waves?
    • more than 1 frequency
    • no harmonic relationship
    • brief duration
    • book dropping
  17. What is a waveform?
    • plot of changes in some variable as a function of time
    • example: displacement, velocity, acceleration, pressure, etc as a function of time
    • can calculate fundamental but cannot easily see all frequency components, or their amplitudes or starting phases
    • graph of amplitude by time (sine wave)
  18. What is an amplitude spectrum?
    • a graphic alternative to the waveform
    • also called the amplitude spectrum in the frequency domain
    • graph of amplitude by frequency
    • shows all component frequencies and their corresponding amplitudes
    • series of discrete lines
    • fundamental always has most amplitude
    • *pg 69 slide 17 and 18
  19. What is the spectral envelope?
    the slope of a spectrum given by connecting the peaks of the vertical lines
  20. What is an octave?
    • doubling of frequncy
    • ratio of 2:1 (up an octave) or 1:2 (down an octave)
  21. What is a line spectrum?
    • energy only at frequencies identified by vertical lines
    • height of vertical line reflects amplitude
  22. What is a continuous spectrum?
    • energy present at all frequencies between certain frequency limits
    • slope of envelope = 0 dB/octave (amp. at all freq., white noise)
    • a slope of 0 dB/octave is not a requirement for continuous spectra
  23. What is a phase spectrum?
    • the phase spectrum in the frequency domain defines the starting phase as a function of frequency
    • the combination of the amplitude spectrum and the phase spectrum defines the waveform completely in the frequency domain
  24. What is a sawtooth wave?
    • complex periodic wave
    • energy at odd AND even integer multiples of fundamental
    • spectral envelope slope of -6 dB/octave
    • *pg 71 slide 25
  25. What is a log scale?
    a distorted scale that makes higher frequencies closer together in order to fit them all on
  26. What is a square wave?
    • complex periodic wave
    • energy only at odd integer multiples of fundamental
    • spectral envelope slope of -6 dB/octave
    • *pg 72
  27. What is a triangular wave?
    • complex periodic wave
    • energy only at odd integer multiples of fundamental
    • spectral envelope slope of -12 dB/octave
  28. What is a pulse train?
    • a repetitious series of rectangularly shaped pulses
    • each pulse has some width or duration (Pd)
    • complex periodic wave with harmonics at odd AND even integer multiples of the PRF (100, 200, 300, etc)
    • amplitude spectrum shows lobes and valleys (nulls)
    • nulls occur at integer multiples of reciprocal of Pd (nulls occur at 1/Pd, 2/Pd, 3/Pd, etc)
    • 1/T defines the pulse repeition frequency (PRF)
    • *pg 73-74
  29. What is white/gaussian noise?
    • an aperiodic waveform with equal energy in every frequency band 1 Hz wide: from -.5 Hz to .5 Hz
    • spectral envelope slope of 0 dB/octave
    • starting phases in random array
  30. Why is white noise called white noise?
    analogous to white light- equal energy in all light wavelengths
  31. *Single pulse pg 74 slide 48
  32. What is signal-to-noise ratio?
    • the ratio of signal level to noise level
    • important for hearing and determining occupational hazards
  33. How do you calculate signal-to-noise ratio?
    • signal level minus noise level
    • positive S/N ratio indicates that signal exceeds noise
    • negative S/N noise exceeds signal; S/N = 0 indicates that noise and signal are equal
  34. What is resonance?
    • the absorption and radiation of acoustical energy by a device
    • frequency dependent
  35. What is the principle of resonance?
    • periodic force (vibrating fork) is applied to an elastic system (hard surface)
    • system is forced to vibrate at frequency of applied force, not at natural frequency of the system
    • the closer the frequency of the applied force to the natural frequency of the system, the greater the amplitude of vibration (loudness increases)- less impedence
  36. What is attenuation?
    a decrease in amplitude
  37. What determines an elastic system's natural/resonant frequency?
    mass and stiffness
  38. When is amplitude of vibration of elastic system greatest?
    when driving frequency equals natural frequency of system
  39. What is a resonance/filter curve?
    • a frequency-selective elastic system
    • it shows the relative amplitude of forced vibrations as a function of frequency that would be realized if driving forces of variable frequency, but constant amplitude, were applied (determines which frequencies will have what amplitude)
  40. What are other names for a resonance curve?
    • filter curve
    • system transfer function
    • amplitude response
    • "frequency response"
  41. What are the two components of impendance?
    • resistance (R)- energy dissipating
    • reactance (X)- energy storage
  42. What components of impedance determine natural frequency?
    • mass reactance and compliant reactance
    • resistance is independent of frequency (does not contribute to determination of natural frequency)
  43. What determines the shape of resonance curve, and location in frequency domain?
    • impedence of resonant system: the relative contributions of resistance, mass reactance, and compliant reactance
    • *pg 80 slide 20
  44. What is a transfer function?
    what we're passing things through
  45. What are the effects of impedance on resonance curve?
    • below center frequency (fc)- compliant dominant
    • above center frequency- mass dominant
  46. What is admittance?
    • refers to the inverse of impedance
    • energy accepted, or admitted, to a system
    • inversely proportional to Z
    • measure in Mho (Z-1)
  47. Why is a narrow tuned system a better generator than a broad tuned system?
    • lower resistance
    • less damping
    • longer free vibrations at natural frequency
  48. Why is a broad tuned system a better receiver than a narrow tuned system?
    • higher resistance
    • more damping
    • brief free vibrations
    • can be forced to vibrate with maximum amplitude over a wide range of frequencies
  49. What is impedance matching?
    • apply vibrating force (driver) to elastic system (load): power transferred to system; system forced to vibrate
    • maximum amplitude occurs at center freq. where Z is minimal and admittance is maximal
    • maximum power transfer occurs when Z of driver = Z of load
  50. What are examples of impedance matching?
    • sounding board of a piano
    • air cavity above the vocal folds: do not amplify sounds, Zs are matched, maximum transfer of power
  51. *Frequency-selective systems: filters pg 82
  52. What are the five principal parameters of filter curves?
    • center (natural) frequency
    • upper cutoff frequency
    • lower cutoff frequency
    • bandwidth
    • attenuation (rejection) rate
  53. Center frequency
    • freqency corresponding to maximum amplitude of vibration
    • mass reactance equals compliant reactance
    • impedance is minimal
    • admittance is maximal
  54. Upper cutoff frequency
    • that frequency above center frequency for which amplitude of response is 3 dB less than response at center frequency
    • the 3-dB down point or the half-power point
  55. Lower cutoff frequency
    • that frequency below center frequency for which amplitude of response is 3 dB less than response at center frequency
    • the 3-dB down point or the half-power point
    • *pg 83
  56. Bandwidth
    • defines the passband of the system: the range of frequencies passed by the filter
    • upper cutoff frequency minus lower cutoff frequency
    • quantifies how narrowly or broadly tuned the filter is
    • measured in Hz
  57. Attenuation rate in dB/octave
    • attenuation rate: roll-off rate, rejection rate
    • the rate at which energy for frequencies less than or greater than center freqency is rejected (attenuated)
    • the slope of the filter curve, expressed in dB/octave
    • *pg 83 slide 42
  58. What are filters?
    • determines which frequencies will be attenuated
    • change amplitudes
  59. What are four types of filters?
    • low-pass
    • high-pass
    • band-pass
    • band-reject
  60. Low-pass filter
    • passes energy below some upper cutoff frequency; attenuates energy above upper cutoff frequency
    • bandwidth equals upper cutoff frequency
    • no lower cutoff frequency (0 Hz)
    • two parameters: upper cutoff frequency and attenuation rate
  61. High-pass filter
    • passes energy above some lower cutoff frequency; attenuates energy below lower cutoff frequency
    • bandwidth = highest freq. in signal minus lower cutoff frequency
    • mirror image of low-pass filter
    • *need higher freq. even though there is no upper cutoff frequency
    • two parameters: lower cutoff freq. and attenuation rate
  62. Band-pass filter
    • passes energy between some lower cutoff frequency and upper cutoff frequency; attenuates energy below lower cutoff frequency and above upper cutoff frequency
    • all five parameters usefal (center freq, upper cutoff freq, lower cutoff freq, bandwidth, attenuation)
    • bandwidth = upper cuttoff - lower cutoff
    • frequency independent
  63. What are two types of band-pass filters?
    • band-pass
    • constant percentage bandwidth
    • *pg 85
  64. Constant percentage bandwidth filter
    • the bandwidth is always a constant percentage of the center frequency
    • dependent on center frequency
    • as center freq. increases, the bandwidth becomes more broad (louder, but not because amplitude increases)
    • *pg 86
  65. *One-octave filter and third-octave filter pg 87 slide 61
  66. Band-reject filter
    rejects energy between some lower cutoff frequency and upper cutoff frequency
  67. White noise
    • all frequencies are represented with some amplitude
    • the more freq. packed together, the higher the amplitude
    • has a pressure spectrum level slope of 0 dB
    • *pg 90 slide 84
  68. Pink noise
    • pass white noise through a specific filter
    • mimics industrial noise (high frequencies)
    • attenuates high frequencies, lets low freq. pass through (opposite of white noise)
    • has a pressure spectrum level slope of -3 dB/octave
    • has an octave-band level slope of 0 dB
  69. Undistorted signal
    the system reproduces the waveform faithfully
  70. Distorted signal
    the shape of the waveform is altered
  71. Frequency distortion
    • change in amplitude
    • *pg 93 slides 4-5
  72. System transfer function
    • the extent to which a signal can be expected to undergo frequency distortion
    • also called amplitude response
    • *pg 93 slide 6
  73. Linear systems
    • alter only the amplitudes and phases of a signal
    • produce frequency distortion
  74. Input-Output (I/O) function of linear system
    • as input amplitude increases output amplitude increases proportionally
    • output amplitude does not need to equal input amplitude; the change is a proportional one
    • *pg 94 slides 8-9
  75. What does transient mean?
    someting in short duration
  76. Transient distortion
    the amplitude response of a sine wave is not really a line spectrum because its duration is finite
  77. Acoustic uncertainty principle
    • change in frequency multiplied by a change in time (always equals some constant, k=1)
    • inversely proportional
  78. What happens as you increase time in an amplitude response?
    • more frequency smearing
    • *an infinite duration is unrealistic (used in a hearing test)
  79. What are effects of duration on amplitude response?
    • energy spread to surrounding frequencies, and amplitude spectrum is continuous
    • nulls at integer multiples of reciprocal of duration (100 ms) 1/.1 = +/- 10 Hz, 2/.1 = +/- 20 Hz, etc (like a pulse train)
    • *pg 94-95
  80. Decay time
    time it takes a signal to go from maximum amplitude to 10% of the maximum amplitude (20 ms)
  81. Rise time
    the time it takes a signal to go from 0 to 90% maximum amplitude (20 ms)
  82. *Rise-decay time pg 95
  83. Amplitude distortion
    • creates frequencies (change in frequency)
    • *pg 95
  84. What happens if some of the instananeous amplitudes of the input signal exceed the limits of linearity?
    • the instantaneous amplitudes at or near max. amp. are "clipped off"- output amp. is not proportional to input amp.- the signal has been peak clipped; distortion
    • more severe peak clipping, more severe distortion
    • output gets messed up, amplitude distortion happens, frequencies are created (complex wave)
  85. Why is amplitude distortion also called nonlinear distortion?
    the distortion arose from operating on the nonlinear portion of the I/O function
  86. What is another name for amplitude/nonlinear distortion?
    harmonic distortion (if the input waveform is sinusoidal)
  87. Percentage harmonic distortion
    proportion of total energy that is undesired energy (important for hearing aids)
  88. How do you calculate percentage harmonic distortion?
    *pg 97 slide 25
  89. Dynamic range
    • difference between amplitude from ENF to its maximum amplitude
    • range we need to stay inside of (linear range)
  90. Electric noise floor (ENF)
    background noise
  91. Intermodulation distortion
    • driving signal is complex (instead of sine wave)
    • experience nonlinear distortion
    • making a complex wave more complex (worse than harmonic distortion)
Card Set
Acoustics exam 2
Acoustics ch 5, 6, 7