Acoustics exam 2

any sound wave that is not sinusoidal

complex waves consist of a series of simple sinusoids that can differ in amplitude, frequency, and phase (called Fourier series)

Fourier Analysis

any complex wave can be decomposed to determine the amplitudes, frequencies, and phases of the sinusoidal components

• periodicity
• complexity

• a wave that repeats itself over time
• also called a periodic time function
• a sine wave is always periodic
• *pg 67 slide 5

• 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

• 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

• 1st (fundamental) = 125 Hz
• 2nd = 250
• 3rd = 375
• 4th = 500
• 5th = 625

• pure tone
• sine wave
• one frequency

• 2 or more pure tones of different frequency, amplitude, and phase added together
• most sounds are complex

• 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

• 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

• more than 1 frequency
• no harmonic relationship
• continuous in time
• "shhhhh"

• more than 1 frequency
• no harmonic relationship
• brief duration
• book dropping

• 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)

• 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

the slope of a spectrum given by connecting the peaks of the vertical lines

• doubling of frequncy
• ratio of 2:1 (up an octave) or 1:2 (down an octave)

• energy only at frequencies identified by vertical lines
• height of vertical line reflects amplitude

• 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

• 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

• complex periodic wave
• energy at odd AND even integer multiples of fundamental
• spectral envelope slope of -6 dB/octave
• *pg 71 slide 25

a distorted scale that makes higher frequencies closer together in order to fit them all on

• complex periodic wave
• energy only at odd integer multiples of fundamental
• spectral envelope slope of -6 dB/octave
• *pg 72

• complex periodic wave
• energy only at odd integer multiples of fundamental
• spectral envelope slope of -12 dB/octave

• a repetitious series of rectangularly shaped pulses
• each pulse has some width or duration (P_d)
• 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 P_d (nulls occur at 1/P_d, 2/P_d, 3/P_d, etc)
• 1/T defines the pulse repeition frequency (PRF)
• *pg 73-74

• 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

analogous to white light- equal energy in all light wavelengths

• the ratio of signal level to noise level
• important for hearing and determining occupational hazards

• 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

• the absorption and radiation of acoustical energy by a device
• frequency dependent

• 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

a decrease in amplitude

mass and stiffness

when driving frequency equals natural frequency of system

• 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)

• filter curve
• system transfer function
• amplitude response
• "frequency response"

• resistance (R)- energy dissipating
• reactance (X)- energy storage

• mass reactance and compliant reactance
• resistance is independent of frequency (does not contribute to determination of natural frequency)

• impedence of resonant system: the relative contributions of resistance, mass reactance, and compliant reactance
• *pg 80 slide 20

what we're passing things through

• below center frequency (f_c)- compliant dominant
• above center frequency- mass dominant

• refers to the inverse of impedance
• energy accepted, or admitted, to a system
• inversely proportional to Z
• measure in Mho (Z^-1)

• lower resistance
• less damping
• longer free vibrations at natural frequency

• higher resistance
• more damping
• brief free vibrations
• can be forced to vibrate with maximum amplitude over a wide range of frequencies

• 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

• sounding board of a piano
• air cavity above the vocal folds: do not amplify sounds, Zs are matched, maximum transfer of power

• center (natural) frequency
• upper cutoff frequency
• lower cutoff frequency
• bandwidth
• attenuation (rejection) rate

• freqency corresponding to maximum amplitude of vibration
• mass reactance equals compliant reactance
• impedance is minimal
• admittance is maximal

• 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

• 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

• 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

• 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

• determines which frequencies will be attenuated
• change amplitudes

• low-pass
• high-pass
• band-pass
• band-reject

• 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

• 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

• 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

• band-pass
• constant percentage bandwidth
• *pg 85

• 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

rejects energy between some lower cutoff frequency and upper cutoff frequency

• 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

• 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

the system reproduces the waveform faithfully

the shape of the waveform is altered

• change in amplitude
• *pg 93 slides 4-5

• the extent to which a signal can be expected to undergo frequency distortion
• also called amplitude response
• *pg 93 slide 6

• alter only the amplitudes and phases of a signal
• produce frequency distortion

• 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

someting in short duration

the amplitude response of a sine wave is not really a line spectrum because its duration is finite

• change in frequency multiplied by a change in time (always equals some constant, k=1)
• inversely proportional

• more frequency smearing
• *an infinite duration is unrealistic (used in a hearing test)

• 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

time it takes a signal to go from maximum amplitude to 10% of the maximum amplitude (20 ms)

the time it takes a signal to go from 0 to 90% maximum amplitude (20 ms)

• creates frequencies (change in frequency)
• *pg 95

• 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)

the distortion arose from operating on the nonlinear portion of the I/O function

harmonic distortion (if the input waveform is sinusoidal)

proportion of total energy that is undesired energy (important for hearing aids)

*pg 97 slide 25

• difference between amplitude from ENF to its maximum amplitude
• range we need to stay inside of (linear range)

background noise

• driving signal is complex (instead of sine wave)
• experience nonlinear distortion
• making a complex wave more complex (worse than harmonic distortion)