Acoustics

Question 1

Duration

Answer 1

how long a sound lasts
- usually measured in ms (0.001 s) or seconds

Question 2

Amplitude

Answer 2

the difference in pressure between compressions and rarefactions
- we generally perceive amplitude as loudness; higher amplitude = louder
- amplitude = pressure

Question 3

Period

Answer 3

the amount of time it takes for a sound wave to complete one cycle of compression and rarefaction
- inversely related to frequency, such that as period increases, frequency decreases
—the longer the time it takes for 1 cycle to occur, the less the frequency of the cycle
- typically measured in seconds or milliseconds
f = 1/T

Question 4

Frequency

Answer 4

the number of times a sound wave cycles from compression to rarefaction in a second
- typically measured in Hz (1/s) or kHz (1000/s)
- perceptual correlate of pitch
f = 1/T

Question 5

Wavelength (λ)

Answer 5

the distance the sound wave travels during one cycle
- usually measured in meters (m)
- requires 1) how fast the wave is moving through the medium, and 2) frequency (how often does the wave cycle?)
- inversely proportional to frequency
- lower frequencies have longer wavelengths, which means that musical instruments and speakers that play low notes need to be bigger
—instruments have to be bigger to allow the low notes to resonate
—speakers have to be bigger to accommodate bigger microphone membranes that can move back and forth

λ = c/f, such that c = the speed of sound
— c = 343 m/s for this class

Question 6

Phase

Answer 6

the point in the cycle for which the sound starts; the orientation of a wave in time
- measured in degrees 0° - 360°
—180° is the opposite phase
—measured in relation to another wave
- we cannot perceive phase, but phase matters for sound interference

Question 7

Pitch

Answer 7

pitch is the perceptual equivalent of frequency.
- the higher the frequency, the higher the pitch

Question 8

Loudness

Answer 8

loudness is the perceptual equivalent of amplitude.
- the higher the amplitude, the louder the sound

Question 9

Hertz

Answer 9

Hertz (Hz) is a measurement used for frequency (or sampling frequency/rate).
- 1/s (one cycle per second)

Question 10

Meters

Answer 10

meters (m) is a measurement of length; for sound, it is used for wavelength
- wavelength is inversely proportional to frequency, such that the wavelength of a sound is the speed of sound through a medium divided by the frequency of the sound

Question 11

Seconds

Answer 11

Seconds (s) is the measurement for time/duration. In the context of sound, it is used to measure duration.
- duration is independent of other factors of sound

Question 12

Degrees

Answer 12

degrees (°) in the context of sound the measurement for phase.
0° is the same phase position as 360°
180° is the opposite phase

Question 13

Complex Sounds

Answer 13

sounds which are made up of more than one component frequency or aperiodic sounds
- wavelength does not look like sine waves
- we make complex sounds by adding two sounds together (producing them at the same time)
—The sum of two waves is the sum of their pressures at any given point

Question 14

Sinusoidal Sound

Answer 14

• sine waves are those which have only one frequency component
• we rarely hear pure tones because noise arriving at the ear is additive; in other words, our experience of sound is usually with multiple events happening at once such that we wouldn’t be truly hearing puretones

Question 15

Sine-Wave Addition

Answer 15

The sum of two waves is the sum of their pressures at any given point.
- When two waves coincide, it is called interference. Interference can be constructive (making the sound stronger) or destructive (making the sound weaker).

Question 16

Phase Cancellation

Answer 16

Phase cancellation is another word for destructive interference, in which a sound becomes weaker due to destructive interference from another sound. Complete phase cancellation (that is, two sounds combining to result in silence) is rare because in order for two sinusoidal sound waves (puretone sounds) to completely cancel each other, they must have the same frequency and amplitude but be at exact opposite phases.
- “Active noise cancelling” headphones use phase cancellation by detecting the sound signal from the outside world via a microphone and inverting it, playing sound that is “out of phase” with it.
—not good at covering up impulse/aperiodic noises
- “Passive noise cancelling” = using physical blocks (i.e. foam) to prevent sound waves from penetrating

Question 17

Constructive Interference

Answer 17

In which a sound is amplified due to sound waves being in phase.
- in phase = peaks and valleys align
- peaks and valleys of a sound wave are another way to say points of rarefaction and compression

Question 18

Destructive Interference

Answer 18

In which a sound is weakened due to sound waves being out of phase
- out of phase = peaks and valleys misaligned
- peaks and valleys of a sound wave are another way to say points of rarefaction and compression

Question 19

Fourier Transform

Answer 19

Fourier Transform is a way of analysing a sound into its component frequencies.

Question 20

FFT and spectra

Answer 20

Fast Fourier Transforms (FFT), or spectra or spectral slices, are models of sound which display the component frequencies and their powers (amplitude) of a sound signal.
- phase is recoverable using FFTs
- FFT and spectra do not show time

Question 21

Spectrogram

Answer 21

Models of sound waves that show time (x-axis), frequency (y-axis), and amplitude/power (darkness).

Question 22

High Pass Filter

Answer 22

Filters which let frequencies higher than a set frequency pass
- “every frequency higher than X may pass”

Question 23

Sound Filters

Answer 23

Filters which determine the kind of frequencies that can “pass” (e.g. be recorded)
- Filters aren’t perfect; they always have a cutoff/slope (rejection rate or roll-off), in which sounds outside of the cutoff are attenuated at a certain rate.
—cutoffs are not vertical (i.e. frequencies that are cut off are never instantly attenuated, such that the waveform will show a vertical line from the cutoff point)

Question 24

Low Pass Filter

Answer 24

Filters which let frequencies lower than a set frequency pass
- “every frequency lower than X may pass”

Question 25

Band Pass Filter

Answer 25

Filters which let only frequencies **within** a set band (range) pass - "every frequency between X and Y may pass"

Question 26

Band Stop / Band Reject / Notch Filter

Answer 26

Filters which let only frequencies **outside** of a set band (range) pass - "every frequency outside of X to Y may pass"

Question 27

Root-Mean-Square (RMS) Amplitude (Amplitude Measurement)

Answer 27

A method that we can use to measure the pressure (amplitude) of a sound wave. **Four steps to RMS**: 1) **measure amplitude of the wave at many points** 2) **square each amplitude measurement** (negative amplitudes will become positive) 3) **take the mean of the squared measurements** 4) **take the square root of the mean** - RMS gets rid of asymmetry and accounts for the fact that sounds can vary in amplitude during their duration

Question 28

Pascal (Amplitude Measurement)

Answer 28

Pascal (Pa) is a measurement that can be used to measure the amplitude/pressure of a sound wave. - Newtons per square meter —N = the force required to move 1 kg 1 m/s per second = 1 kg * m/s² - 0.00002 Pa is the lowest audible amplitude

Question 29

the Planck Pressure

Answer 29

The theoretical maximum pressure in the smallest possible area; 1 Planck force per 1 Planck area —4.633*10¹¹³ Pascal —For comparison, the loudest possible waves in Earth's atmosphere are 1.01*10⁵ Pascal

Question 30

dB SPL

Answer 30

**dB SPL** (decibel pressure sound level) is a decibel measurement that uses human hearing as a reference point, in which 0 dB SPL = the lower threshold of human hearing, or the softest sound that we can hear. - uses a **logarithmic scale** **0 dB SPL = 0.00002 Pa** To calculate dB SPL from Pa, use the following equation: dB SPL = 20*log₁₀(Pascal/0.00002) - 140 dB is the highest tolerable sound we can hear *with* pain - 120 dB causes hearing damage instantly - human conversation is around 20 dB SPL - **dB SPL can be negative**

Question 31

dB HL

Answer 31

**dB HL** (decibels of hearing loss) is a measurement of sound amplitude/pressure that uses human hearing threshold *at each specific frequency* as a reference point. In other words, 0 dB HL is different for any given frequency. - 0 dB HL = the faintest sound of a certain frequency that a normal human can perceive —0 dB HL at 100 Hz is not the same as 0 dB HL at 200 Hz when thinking in terms of dB SPL, however perceptually we will sense these two at the same volume. - Motivated by the fact that human sound detection is frequency dependent - Hearing tests are conducted in dB HL

Question 32

Quantization

Answer 32

Measuring and storing values of a sound wave - aka **digitization**, **discretization**, or **sampling** - we cannot store the exact curvature of a wave, so we take samples of the sound wave (i.e. amplitude) to be able to recreate those pressure variations via playback - quantization does not create analog recordings

Question 33

Sampling Rate

Answer 33

the rate at which samples are taken, typically measured in Hz (samples per second); how many samples are taken per second - Sampling at too low of a sampling rate can cause significant portions of data to be lost —to faithfully capture a sound, sample at minimum 2x the highest frequency of the desired signal (**Nyquist Theorem**)

Question 34

Nyquist theorem

Answer 34

The highest frequency that can faithfully be captured by a sample signal is 1/2 of the sampling rate —For example, if the sampling rate is 10,000 Hz, the highest frequency that can be faithfully captured in the sample is 5,000 Hz

Question 35

Nyquist frequency

Answer 35

the frequency of 1/2 of the sampling rate

Question 36

Compression of Audio

Answer 36

Storing sound in limited space —**lossy**: Cutting out or "throwing away" data from a sound sample in order to create a smaller sound file —**lossless**: keeps all the data —lossy audio compression is attuned to human perception

Question 37

Bitrate

Answer 37

The number of bits required to capture a second of audio - **kpbs (kilobits per second)** - Variable bitrate (**VBR**) - Lower bitrate = more compression

Question 38

Codec

Answer 38

Short for "code-decode," **codec** are methods of encoding and decoding audio. - many modern devices/software (i.e. cellphones, zoom, bluetooth) use lossy codecs (codecs which strategically leave out data) —lossy codecs are attuned to human perception, such that they try to preserve information that is relevant —For example, "hold music" over the phone sounds terrible because phone calls are attuned to human speech, not to music —**Lossy compression throws away data such that when it's gone, it's gone, it's gone, it's gone.** - Mariah Carey

Question 39

Noise Reduction

Answer 39

A method of filtering audio such that non-target sound is cut out —video call apps (i.e. Skype, Zoom) uses noise reduction software to remove non-target speech & sound; they're usually trained on language data, which can create issues if the language you're using wasn't included in the training

Question 40

Which fundamental properties of sound are related, and which change independently of one another?

Answer 40

Frequency, wavelength, and period are related. Frequency is inversely proportional to period: **f = 1/T** Wavelength is inversely proportional to frequency: **λ = c/f**, such that c = the speed of sound Duration and amplitude change independently of these properties.

Question 41

What makes a complex wave complex?

Answer 41

Complex waves are those which have multiple component frequencies. They are also aperiodic waves.

Question 42

Why does phase cancellation work?

Answer 42

Phase cancellation works because it depends on matching air particle compression with rarefaction. In other words, in order to make a sound's amplitude (pressure) lower, one can match it with a sound wave of equal amplitude & frequency, but with opposite 180° phase. This would allow the compressed points of the sound wave to match up with the decompressed points (rarefaction) of the opposite sound wave, thus cancelling the compression out and bringing particles to (theoretically) equilibrium.

Question 43

How do we find the frequencies and phases of components of a complex wave?

Answer 43

We can use Fourier Analysis or FFT (Fast Fourier Transform) to create spectra. Spectra show the component frequencies of a sound wave in addition to their powers (amplitude).

Question 44

Why would we say that the basilar membrane acts like a fourier transform?

Question 45

Why do we combine waves using addition, rather than multiplication?

Answer 45

The result of combining two waves is the sum of their pressure at any given point. Sound waves are essentially patterns of particle disturbances.

Question 46

Which basic characteristics of sound are humans sensitive to through hearing?

Answer 46

Humans are sensitive to amplitude as loudness, and we perceive frequencies as pitch (from frequency, we can derive the wavelength and period of a sound, but these are less intuitive so we typically think of pitch in terms of frequency). However, we have no way of perceiving phase.

Question 47

Why do constructive and destructive interference happen in sound? Answer from the ‘compression and rarefaction’ perspective.

Answer 47

Compression + compression = more compression Compression + rarefaction = less compression rarefaction + rarefaction = more rarefaction Constructive and destructive interference are ways of describing how two (or more) sound waves can combine and create stronger or weaker sound signals. They rely on the principle that the combination of two sound waves is the sum of their pressure at any given point.

Question 48

What’s the relationship between fourier spectra and spectrograms?

Answer 48

Fourier spectra capture component frequencies and their powers (amplitude) in a sound signal, but they do not capture time. Spectrograms capture frequency, amplitude, and time. They can essentially be thought of as many, many spectra lined up next to each other to create a 3D model, that is then turned into a 2D model where the x-axis is time, the y-axis is frequency, and darkness/saturation is amplitude.

Question 49

Why would one consult an FFT spectrum versus a spectrogram? What information is exclusively/best visualized from each?

Answer 49

A spectrogram shows the duration of the sound signal/sample, but it does not show exact measurements for amplitude at a given frequency (it shows amplitude as darkness). It shows a "continuous" appearing measurement of frequency along time, where the dark parts signify any sound captured in the sample. They are good for visualizing the amplitude and frequency of a sound signal through time. On the other hand, the FFT spectrum will show the component frequencies of a sampled sound signal as well as their amplitudes, leaving out time. FFT spectra are not good for visualizing the duration of a sound signal. Overall, it depends on what you're focused on.

Question 50

Why does the distance from the source matter for amplitude measurement?

Answer 50

Sound fades over a distance: **if the distance from the sound is doubled, pressure will be cut in half**. - Moving the medium that a sound is travelling through will dampen the sound - Technically, any sound is "safe" for hearing (it just depends on how far you are)

Question 51

Why don’t we use Pascal to measure and discuss amplitudes in daily life?

Answer 51

Pascal (Pa) works to measure amplitudes, however the quietest sound a human can hear (0 dB SPL) is equivalent to 0.0002 Pa. Human conversation sits at around 0.002 Pa, and 20 Pa is enough to cause instant hearing damage. Our sound tolerance and many everyday sounds that we hear sit in a range that is not well-described by Pa, such that it Pa is not the most efficient way to discuss amplitudes of sounds we hear in daily life.

Question 52

What are the relative levels of risk for different amplitudes of sound? E.g. What’s ‘safe’, ‘safe for a limited time’, and ‘never safe’?

Answer 52

**dB SPL**: safe: <70 dB safe for <8 hours: 70-85 dB (then 85-90 dB exposure time is 1/2 for every 3 dB) *never safe for any amount of time*: 120+ dB - **sounds over 132 dB can rip the organ of corti off of the basilar membrane** - long term high amplitude sounds can damage stereocilia and cause cell death

Question 53

Explain what a microphone and speaker do, in terms of transduction from one type of signal to another?

Answer 53

Microphones and speakers transduce pressure variations in the air (sound waves) into mechanical waves, into electrical signals. Dynamic microphones have a **membrane** that moves when hit with air pressure waves. The membrane moves a coil of wire around a magnet. This then creates an electric signal that carries the pattern of pressure variations that we want. Speakers are almost the opposite of this process. In a speaker, there is a coil of wires wrapped around a magnet. When electric signal passes through the coil, the magnet vibrates, causing a cone around the coil to vibrate. The vibration of the cone creates the pattern of air pressure variations that we want.

Question 54

Why do we have to quantize sound to capture it with computers?

Answer 54

Computers deal with binaries. They are "digital," whereas sound waves are "analog." In other words, they store discrete information (in various amounts of precision). We have to quantize sound in order to store it digitally.

Question 55

Explain what a sampling rate is

Answer 55

A sampling rate is the number of samples (of a sound wave) taken per unit of time (usually 1 second, so sampling rates are in Hz or 1/s). In other words, it is how often the specific pressure of a sound wave is measured during one second.

Question 56

Explain the effects that using too low of a sampling rate has on captured audio

Answer 56

Using too low of a sampling rate will not faithfully capture the sound being sampled, leaving out crucial information and creating a waveform that is a far misrepresentation of the actual sound signal.

Question 57

Explain why lossy compression is referred to as ‘lossy’

Answer 57

Lossy compression is that which strategically "throws away" information from an audio file. It is "lossy" because once lossy compression is performed, there is a "loss" of information. Lossy compression is useful for storing audio in a limited amount of space/file size, or transporting audio.

Question 58

Explain the difference between ‘bitrate’ and ‘sampling rate’ for a compressed digital audio signal.

Answer 58

Bitrate: Sampling rate: measured in Hz, number of samples taken per second

Question 59

What’s the speed of sound, roughly?

Answer 59

The speed of sound in air is roughly 343 m/s.