1. Encoding and Simple Manipulation
Sound: Introduction
Encoding and Simple Manipulation

2. Sound is made when something vibrates
Air molecules oscillate back and forth from their equilibrium position, affecting their neighbors

3. Sound waves are pressure waves
As molecules oscillate back and forth, areas of high and low pressure occur
Called compressions and rarefactions, respectively

4. Sound waves are longitudinal
Motion is parallel to direction of energy transport
Representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal nature of the pressure-time fluctuations

5. Sound waves are longitudinal
Plot pressure fluctuations over time encountered by a fixed detector

6. Properties of sound waves
Frequency: cycles per second (Hz)
Amplitude: distance from 0

7. Psychoacoustics: Human Perception of Sound
Ear serves as transducer: coverts sound energy to mechanical energy to nerve impulse transmitted to brain

8. Psychoacoustics: Human Perception of Sound
Pitch
Loudness
Timbre

9. Psychoacoustics: Human Perception of Sound
Pitch – frequency
Loudness – amplitude
Timbre – combination of various frequencies

10. Pitch Humans hear frequencies between 20 Hz and 20,000 Hz
 frequency =  pitch

11. Pitch Humans hear frequencies between 20 Hz and 20,000 Hz
 frequency =  pitch
Hearing works on ratios for pitch…
We hear difference between 200 Hz and 400 Hz, the same as 500 Hz and 1000 Hz

12. Loudness
Perception of volume is related logarithmically to changes in amplitude
 amplitude =  pitch

13. Loudness
If one sound is 10x times more intense than another sound, then it has a sound level which is 10*x more decibels than the less intense sound.
Intensity is very objective quantity; can be measured with sensitive instrumentation
Loudness is more subjective response; will vary with a number of factors (e.g. age, frequency)

14. Decibel is a logarithmic measure
A decibel is a ratio between two intensities: 10 * log10(I1/I2)
As an absolute measure, it’s in comparison to threshold of audibility
0 dB can’t be heard.
Normal speech is 60 dB.
A shout is about 80 dB

15. Digitizing Sound
Analog-to-digital conversion: measure amplitude at an instant as a number
Instantaneous measure is called a sample

16. Understanding how computers represent sound
Consider how a film represents motion…
Movie is made by taking still photos in rapid sequence at a constant rate, usually twenty-four frames per second
When the photos are displayed in sequence at that same rate, it fools us into thinking we are seeing continuous motion, even though we are actually seeing twenty-four discrete images per second

17. A collection of still frames

30. How computers represent sound
Digital recording of sound works on the same principle
We take many discrete samples of the sound wave's instantaneous amplitude, store that information, then later reproduce those amplitudes at the same rate to create the illusion of a continuous wave

31. How often should we take samples?
sampling rate: number of samples taken per second
Nyquist Theorem: need to take twice as many samples as the highest frequency we wish to record
Sampling rate = 2 * max sound wave frequency

32. How often should we take samples?
sampling rate: number of samples taken per second
Nyquist Theorem: need to take twice as many samples as the highest frequency we wish to record
Sampling rate = 2 * max sound wave frequency
CD quality is 44,100 samples per second
what is the max frequency a CD can represent?

33. Nyquist Theorem
Consider a graph of a 4,000 Hz cosine wave, being sampled at a rate of 22,050 Hz
Sample is taken every milliseconds

34. Nyquist Theorem Consider same 4,000 Hz cosine wave sampled at 6,000 Hz
Sample is taken every milliseconds
Wave completes more than 1/2 cycle per sample

35. Digitizing sound with the computer: bit depth
The range of possible sample values depends on the number of bits used to store each sample
Common bit-depths: 8 and 16

36. 16 bits per sample: +/- 32K
Each sample can be between -32,768 and 32,767
Why such a bizarre number?
Because 32, , = 216
< 0
i.e. 16 bits, or 2 bytes
> 0
Compare this to for light intensity
(i.e. 8 bits or 1 byte giving us 256 different values)

37. Properties of sound Sound wave Frequency Amplitude Wavelength Period
Digitized sound
Sampling rate
Bit depth
Playback rate