Measurement and Specification of Sound
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Five major aspects of the decibel
 Ratio
 Logarithm
 Nonlinear
 Relative unit of measure
 Expressed in terms of Reference Levels

What is the faintest sound which the auditory system can respond?
 20 μPa  pressure
 10^12 W/m^2  intensity

What is the dynamic range of the auditory system?
Express as a ratio
 14bels
 In absoulte terms = 10^14
 140 dB

Complete:
1 bel =
 log I1 / Io
 = log 10^2 / 10^12
 = log 10^14
 = 14

Complete:
1 bel = ___dB
10

Complete:
The ratio of 2 intensities expressed in dB is ____
 A bel = log I1 / Io
 10dB
 100:1

Complete:
The ratio of 2 sound pressures expressed in dB is _____
 decibel = 20 log p1 / po
 140dB
 10:1

When calculating dB intensity level (dBIL), what reference is used?
 dB IL = 10 log I1 / 10^12 W/m^2
 What is dB IL of 10^8 W/m^2
 dB IL = 10 log I1 / 10^12 W/m^2
 = 10 log 10^8 / 10^12
 = 10 log 10^4
 = 10 (4)
 = 40 dB IL

When calculating dB sound pressure level (dB SPL), what reference is used?
 dB SPL = 20 log p1 / 20 μPa
 dB SPL = dB IL
 What is the dB SPL of 200 μPa?
 dB SPL = 20 log p1 / 20 μPa
 = 20 log 200/20
 = 20 log (10)
 = 20 (1)
 = 20 dB SPL
 200 μPa is 20 dB greater than the reference of 20 μPa.

Why is the decibel considered nonlinear?
Because the decibel involves logarithms which are inherently nonlinear

Complete:
If intensity is increaed by a factor of 2, overall intensity will increase by _____ dB
20

Complete:
If sound pressure is increased by a factor of 2, overall sound pressure will increase by ____ dB
20

What are the basic components of a sound level meter?
 Microphone  a transducer that converts variations in sound pressure into an electrical signal. Transduces acoustic energy into electrical energy.
 Amplifier  a device that increases the low voltage electrical signal from the microphone
 Attenuator  sound level meters are used for measuring sounds that vary greatly in sound level (approx. a 140 dB range). An attenuator is used to adjust for the wide range of sound levels that are measured. Reduces the amplification from the maximum provided by the amplifier
 Weighting networks  the sound level meter has a number of weighting or "filtering" networks. The weighting networks allow the response at various frequencies to be controlled
 Output meter  after the electrical signal from the microphone is amplified, attenuated, and filtered, it is directed to an output meter. The RMS value of the signal is indicated. The meter is calibrated in decibels above a reference of 20 μPa (i.e. dB SPL). The attenuator is calibrated in bels (i.e. 10dB steps)

Define periodic vibration.
What are the types of periodic vibration?
 A waveform that repeats itself.
 Simple Periodic Vibration: Sinusoidal Vibration
 Complex Periodic Vibration: Contains more than one sinusodial component

Define aperiodic vibration.
Waht the the 2 types of aperiodic vibration?
 A waveform that does not repeat itself
 Transient Vibration: a waveform that occurs once and only once
 Random Vibration: a waveform that is continuous, but not repetitive

Define the concept of a filter.
What are the 3 basic types of filters?
 The spectrum of a sound can be influenced or shaped by a device called a filter. A type of resonator. Allows certain frequencies to pass through it; the filter will vibrate at only certain frequencies. A device which selectively passes through certain frequencies
 Lowpass filter  will pass all sinusoids with frequencies below a particular value
 Highpass filter  passes sinusoids with frequecies above a particular value
 Bandpass filter  passes all sinusoids with frequencies between 2 particular values

Define cutoff frequency and rejection rate of a filter.
 Cutoff frequency  frequency values above, below, or between which the filter passes sinusoids without reducing their amplitude significantly. The frequency at which power output has decreased by onehalf.
 Rejection rate  refers to how rapidly the filter rejects or attenuates amplitude above or below the cutoff frequency. Reported in dB/octave
 1 octave above = 2 fo
 1 octave below = 1/2 fo
 Example 1:
 Consider the following example. A lowpass filter has a cutoff frequency of 1000 Hz. Rejection rate is 30 dB/octave. This indicates that the filter reduces amplitude by 30 dB for each octave above 1000 Hz. For example, the amplitude will be reduced by 30 dB at 2000 Hz. The amplitude will decrease another 30 dB at 4000 Hz. Etcetera.
 Example 2:
 You have two highpass filters with cutoff frequencies of 2000 Hz. One has a rejection rate of 30 dB/octave. The other has a rejection rate of 100 dB/octave.Which attenuates amplitude more rapidly when frequency is decreased below the cutoff frequency? 100 dB/octave.

Briefly describe 2 ways in which filters can be used.
 To "shape" spectra of signals
 To determine the frequency spectra of unknown signals

Peak amplitude
 Ap
 The largest absolute value of amplitude (either positive or negative) achieved over time

Peaktopeak amplitude
 App
 Measured from the largest positive peak to the larges negative peak achieved over time
 App = 2Ap

RMS amplitude
 RootMeanSquare
 Arms
 A commonly used "average" amplitude. Three processes are involved when determining RMS amplitude
 1. Square each instantaneous amplitude. (All negative values become positive.)
 2. Compute an average of the squared instantaneousamplitudes.
 3. Compute the square root of the average.
 Arms = 0.707 x Ap

Fourier analysis
mathematical analysis of a complex waveform into its component sinusoids

Spectrum
amplitude as a function of frequency (i.e. analysis of sound in frequency domain)

Fundamental frequency
 Hz
 Of a complex periodic quantity: corresponds to the period of that periodic vibration. The frequency of the sinusoid that has the same period as the periodic quantity. Time Domain
 1/period(s)
 Of a series of sinusoids: their largest common multiple (or divisor). Frequency Domain

Harmonics
 integer multiples of that frequency
 1st harmonic fo
 2nd harmonic 2 x fo
 3rd harmonic 3 x fo
 4th harmonic 4 x fo

Line spectrum
 characteristics of periodic waveforms
 the spectrum consists of discrete lines at various frequencies

Continuous spectrum
 characteristics of aperiodic waveforms
 there is a continuous distribution of energy across frequency