BIOS 1163: Speech Physics

what is voice in physic terms?

sound wave generated by vibration of the vocal cords

sound waves require what 2 things? what must molecules in the second part have?

1. Vibrating Element: which is immersed in a conducting medium

2. Conducting Medium: the material which through the sound waves propagate >> mostly gas, then liquid or solid

Molecules in a conducting medium must have:

1. Elasticity: allows the medium to resist deformation + generate a restoring force that returns it to its equilibrium. This causes the medium to vibrate > key in the transmission of sound waves

2. Mass: required for energy transfer > one mass collides with another = transfer of energy > propagation of sound over distance

what is a vibration?

oscillatory motion about an equilibrium position

• Occur naturally when a particle (physical system) is displaced from its equilibrium > restoring forces act to return it back

• Restoring force: directed towards equilibrium, ↑ with displacement

what is the difference between periodic and aperiodic waves?

Periodic Vibrations	Aperiodic Vibrations
Regular + repeating in time Simplest form = simple harmonic motion  Produce fundamental frequencies + harmonics	Irregular + non-repeating No consistent frequency Produces complex, irregular waveforms “noise” = sounds produced by an aperiodic vibration
Vowels	Many consonant sounds  e.g /s/ = “snake”, /f/ = “fish”

what is sound?

Series of pressure changes that our ear can detect

how do humans produce sound waves?

1. Air pressure system to produce air flow → respiratory system = exhaling places the conducting medium (air) into the sound tract

2. Vibrating element → vocal folds = modify the flow of air by vibrating / creating vibrations in the surround air

3. Resonating system → vocal tract (incl. Larynx, pharynx, oral cavity + nasal cavity) = resonates + shapes sound waves

what is simple harmonic motion?

) type of periodic motion where an object moves back and forth about an equilibrium position under a restoring force that is directly proportional to its displacement

F = -kx    
produces a sinusoidal waveform

• Pure tones (e.g single musical note) are produced by SHM

what is displacement?

Distance of object from its equilibrium position (in metres)

what is amplitude?

Maximum displacement (metres)

• Greater amplitude = loudness

energy of vibration =

• Energy of a vibration = amplitude²

what is wavelength?

Distance b/w successive crests of a wave (metres) = cycle length

what is the period?

The time for 1 completed vibration (or cycle, in seconds)

• Not dependent on amplitude, only dependent on physical properties = mass + stiffness 

• Measured from one crest to another / or 1 trough to another

what is frequency? and its link to pitch? and how the humans make it?

Number of completed vibrations in one second → measured in cycles / second (Hz)

• Frequency = reciprocal of the period: F = 1/T

• Determines the pitch: directly proportional

• Low frequency = low pitch

• High frequency = high pitch

• Vocal folds wiggle 100 times / sec > produce puffs of air with frequency of 100 beats / sec (Hz)

• Additional motions of the vocal folds (e.g collisions with each other) create additional frequencies – harmonics at 200Hz, 300Hz …

what is velocity?

Speed at which the disturbance travels through the medium / speed at which the sound wave travels in the air

V = distance / time

For a wave: one wavelength (distance)  / one period (T)

V = λ / T,  f = 1/T hence: v = fλ

• V = wave velocity (ms^-1)

• F = frequency (Hz)

• λ = wavelength (m)

what happens to sound as it travels through different mediums?

• Velocity of sound is the same for all frequencies in one medium

• Once a sound wave is produced, the frequency / pitch does not change as it travels through different media

  • HOWEVER, the speed of sound (velocity) + wavelength in that medium will change

  • E.g v _sound of a rock = 5100ms^-1

what are factors that influence sound wave velocity? for all solids / gases / liquid mediums

1. Elasticity (rigidity): ↑ elasticity (or stiffness), faster the wave propagates

2. Density (mass): ↑ density, slower the wave velocity

If medium is:

• Solid: faster speed

• Liquid: intermediate speed

• Gases: slower speed

If the Medium is Gaseous: velocity of sound is affected by temperature + humidity

• NOT affected by pressure:

1. Temperature: ↑ Temp = ↑ elasticity, ↓ density = ↑ velocity

• Increases by ~0.6ms^-1 for each 1^oC  increased

2. Humidity: ↑ humidity = ↓ air density = ↑ velocity of sound

• Density = mass / volume 

• Humidity is water vapour → mass of water < mass of air ∴ humidity reduces air density

how do humans hear sounds?

1. Pressure reaches our ear 

2. cause the ear drum (tympanic membrane) to vibrate 

3. vibrations transmitted through middle ear bones > to cochlea (inner ear) 

4. In the cochlea: basilar membrane carries hair cells > different regions of this membrane move in response to different f(x)

5. The movement bends hair cells in that region > stimulates the attached auditory nerve fibres

6. Different neurons are activated = perceive pitches

define harmonics / resonance / timbre / pitch

Harmonics	Sinusoidal waves where that is related to a fundamental frequency (f) as an integer multiple = 2f, 3f etc.
Resonance	The quality of a sound being full / reverberating  he frequencies travel through the vocal tract > depending on the shape of the tract, it resonates with certain harmonics  = vocal tract amplifies those resonant harmonic frequencies >> louder
Timbre	quality, "color," or texture of a sound that allows the ear to distinguish between two sounds with the same pitch and loudness
Pitch	the perceptual quality of a sound that allows us to classify it as "high" or "low."

what is natural frequency?

the frequency at which an object naturally vibrates without any external influence

• All objects have a natural tendency to oscillate when particles are displaced from their equilibrium position

• E.g just pushing a child on a swing normally, after it reaches its amplitude

• Natural Vibrations in the Human Body:

  • Head or Neck: ~ 30Hz 

  • Eyeball: ~ 80Hz 

  • Vocal Folds: ~ 125Hz (male), ~ 210Hz (female), ~>300 Hz (child)

what influences natural frequency?

Determinants of Natural Frequency: determined by mass / restoring forces → stiffness / tension / length

• Longer an object = lower the fundamental frequency

• Greater the mass = lower the fundamental frequency

• More stiff / tense an object = higher the fundamental frequency

what are some examples of natural frequency ?

• Guitar String: longer string = lower f, thicker string = lower f, tighter string = higher f

• Tuning Fork: the vibrating tines generate a sound wave

  • Longer tines = lower f, greater mass = lower f

• Flute: the longer the air column = lower f

what is forced vibrations?

(Def.) external periodic force drives the object = causes oscillation at the frequency of the applied force rather than its natural frequency

• E.g you move the bars of the swing by yourself

explain based on the driving frequency and the natural frequency when an energy transfer is efficient?

• If driving f goes further from natural f → energy transfer is inefficient + oscillations are small

• If driving f comes closer to natural f → energy transfer increases + amplitude becomes larger

• If driving f = natural f→ maximum energy transfer = RESONANCE

looking at a frequency-response curve, what is the natural frequency? what is its shape? its bandwidth?

1. What is the natural frequency in the system (f₀)

2. What is its shape? 

• Narrow peak = responds strongly to a specific frequency

• Wide peak = responds to a broader range of frequencies

3. Bandwidth: how selective a resonant system is

• Large bandwidth = not good for clear enunciated sounds

• To calculate: find peak power, half it draw line there / Find points of intersection with graph = draw lines down = gives the range of the bandwidth / bandwidth = biggest - smallest

what is resonance?

occurs when an object vibrates in response to an applied periodic force whose frequency = object’s natural frequencies

• Most vibrating systems have multiple resonant frequencies

• When driven by complex / random vibrations → objects tend to vibrate at the resonant f >> acts as a filter

• Resonance > produces very large oscillations when energy is continuously added at the right f

  • E.g the Tacoma Bridge > the wind was continuously blowing > the oscillations of the bridge increased

what is damping? what is the damping effect in air and water? is the period affected? what is affected?

energy is removed from a vibrating system (like frictional effects) = causes oscillations to decrease in amplitudes

• Makes f less sharp + more broad

• In sound amplitude = loudness

• The period is NOT affected = the frequency + pitch of a sound wave will not change

• In the air = relatively low friction = damping is low 

• In water = higher friction = damping is greater

what is superposition of a wave? and its 2 resultant waves?

when 2 or more waves meet, their displacements combine to form a new wave

• The resulting wave = sum of individual waves

Resultant Wave:

• Constructive Interference: Waves add together = larger amplitude

• Destructive Interference: Waves cancel = smaller / zero amplitude

  • How noise cancelling headphones work

what is a beat?

Occurs when 2 sound waves of slightly different f combine = produces an interference wave whose amplitude varies over time = characteristic pulsing / throbbing sound

what is a progressive wave?

Moves through a medium, transfers energy from one place to another continuously

All particles oscillate with same amplitude and frequency

Pressure waves travel through the air  > In a perfect case, it would continue for ever  HOWEVER, in reality the amplitude reduces + damping = gradually stops

what happens if a progressive wave encounters a boundary?

@ Boundary: wave encounters a boundary =  part (or all) of the wave is reflected.

• Produces two waves in the medium: incident (travelling towards) and reflected wave

• These waves move in opposite directions

• pass through each other =  they superpose = regions of constructive and destructive interference.

what is a standing wave? how is it formed? what are the particles doing? what frequencies are needed? how is each standing wave measured in terms of wavelength?

Standing Wave

formed by the interference of two progressive waves moving in opposite directions Remains confined, storing energy without transferring it forward No net movement of wave through the medium

Particles oscillate with different amplitudes, same frequency Node = place of no displacement Anti-node = place of maximum displacement You can have more / less nodes and anti-nodes based on how fast the frequency is

For a standing wave to occur: formed by the interference of two progressive waves moving in opposite directions The incident + reflected waves continuously superpose = requires continuous vibration reflected within a confined space HOWEVER,only  stable @ specific frequencies: Frequencies: 20, 40, 60 Hz Here, the wave is amplified = produces resonance Wavelength has to = the distance b/w fixed ends > so there is a node at both ends = distance between the fixed ends needs to be a whole number of "half-wavelengths”.

what are transverse waves?

• Molecules in the wave move at right angles to (or across) the direction of the wave (BASICALLy move up and down)

• Medium must be able to support sideways force & transfer this energy to neighbouring molecules

  • possible in solid objects

  • Possible on the surface of liquids

  • NOT possible in gases

what are longitudinal waves?

• what sound waves are

• molecules oscillate in the same direction to the wave’s direction of travel (sideways)

• Forms regions of compression and rarefaction

• ALL solids, liquids and gases have these properties