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Five major aspects of the decibel
- Ratio
- Logarithm
- Nonlinear
- Relative unit of measure
- Expressed in terms of Reference Levels
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What is the faintest sound which the auditory system can respond?
- 20 μPa - pressure
- 10^-12 W/m^2 - intensity
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What is the dynamic range of the auditory system?
Express as a ratio
- 14bels
- In absoulte terms = 10^14
- 140 dB
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Complete:
1 bel =
- log I1 / Io
- = log 10^2 / 10^-12
- = log 10^14
- = 14
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Complete:
1 bel = ___dB
10
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Complete:
The ratio of 2 intensities expressed in dB is ____
- A bel = log I1 / Io
- 10dB
- 100:1
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Complete:
The ratio of 2 sound pressures expressed in dB is _____
- decibel = 20 log p1 / po
- 140dB
- 10:1
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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
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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.
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Why is the decibel considered nonlinear?
Because the decibel involves logarithms which are inherently nonlinear
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Complete:
If intensity is increaed by a factor of 2, overall intensity will increase by _____ dB
20
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Complete:
If sound pressure is increased by a factor of 2, overall sound pressure will increase by ____ dB
20
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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. 10-dB steps)
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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
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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
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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
- Low-pass filter - will pass all sinusoids with frequencies below a particular value
- High--pass filter - passes sinusoids with frequecies above a particular value
- Band-pass filter - passes all sinusoids with frequencies between 2 particular values
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Define cut-off frequency and rejection rate of a filter.
- Cut-off 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 one-half.
- Rejection rate - refers to how rapidly the filter rejects or attenuates amplitude above or below the cut-off frequency. Reported in dB/octave
- 1 octave above = 2 fo
- 1 octave below = 1/2 fo
- Example 1:
- Consider the following example. A low-pass filter has a cut-off 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 high-pass filters with cut-off 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 cut-off frequency? 100 dB/octave.
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Briefly describe 2 ways in which filters can be used.
- To "shape" spectra of signals
- To determine the frequency spectra of unknown signals
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Peak amplitude
- Ap
- The largest absolute value of amplitude (either positive or negative) achieved over time
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Peak-to-peak amplitude
- Ap-p
- Measured from the largest positive peak to the larges negative peak achieved over time
- Ap-p = 2Ap
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RMS amplitude
- Root-Mean-Square
- 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
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Fourier analysis
mathematical analysis of a complex waveform into its component sinusoids
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Spectrum
amplitude as a function of frequency (i.e. analysis of sound in frequency domain)
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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
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Harmonics
- integer multiples of that frequency
- 1st harmonic fo
- 2nd harmonic 2 x fo
- 3rd harmonic 3 x fo
- 4th harmonic 4 x fo
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Line spectrum
- characteristics of periodic waveforms
- the spectrum consists of discrete lines at various frequencies
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Continuous spectrum
- characteristics of aperiodic waveforms
- there is a continuous distribution of energy across frequency
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