Lecture 1 Flashcards
What is the One-Mass model?
Like mass and spring, in the trachea. Muscles create resonance; pressure built up due to narrowing in the trachea. Waves create a fluctuating high to low pressure.
In One-Mass model, what does condensation and rarefaction mean?
High pressure area - condensation (narrowing at trachea)
Rarefaction - less condensation (low pressure area)
What are the components of sound production?
Transduces electrical energy into mechanical energy - pressure wave set up with motion, sinuisoidal wave created.
Increase in volume = decrease in pressure.
What is sound?
In terms of vibration,
Vibration - movement of object from one point to another point in space, and usually back to the first point. Must produce a sound wave in a medium - leads to hearing (air)
What is sound? In terms of auditory sensation
Auditory Sensation - produced by alteration in pressure, particle displacement or particle velocity which is propagated in an elastic medium through the ear
What is the mass-spring system?
Molecules in the air, elastic collisions can change how these move in space
Molecule bounce through the spring system.
Transfer of energy in springs, they compress and expand from pushing of mass.
Pressure waves transferred by molecules
What is simple harmonic motion?
When an object, displaced from its equilibrium position, is acted on by a force proportional to the displacement, object will undergo a periodic motion, which, in the absence of friction is….
Ex. Springs and masses that pull and let go - move in sinusoidal fashion
What force is periodic motion controlled by?
Resistance (R): forces associated with friction “waste” energy and eventually causes the motion to stop. Turns energy of vibrating motion into heat
What are another 3 forces periodic motion is controlled by?
Inertia: Is a property of matter. Once moving, the body will “want” to continue moving; if at rest the body will stay at rest unless acted upon by some force.
Stiffness = 1/elasticity; force that depends on how much displacement there is.
F = -kx (Hooke’s Law) (k = spring constant, x = displacement) - restoring force of spring when mass is displaced.
Free Vibration of a Simple Mass and Spring System
What happens to spring at rest?
What happens at t=0?
What happens at t>0?
Rest: spring not stretched or compressed, applies no force.
t=0: free vibration, no external forces applied after t>0. (F = ma)
Oscillations will continue with same acceleration as time passes, eventually traces sinusoid. (Natural/Resonant frequency = f = √( k / m ))
What are the three forces that control periodic (vibratory) motion?
Resistance (R)
Inertia
Stiffness
In the oscillation of 3 masses, which one will have the highest frequency? Why?
Smallest mass =highest frequency.
Frequency of vibration proportional to √ of stiffness or restoring force and inversely proportional to √ of mass.
Mass x4 = 1/2 frequency; stiffness x4 = 2x frequency
What is a sinusoid? Why should we care?
Mathematical equation describing a curve with the form of a sine wave. Sum of sinusoids is a combination of waves.
Describe the responses of many simple physical systems (mechanical and acoustical ones relevant to speech and hearing).
More complex signals can be represented by sum of many sinusoids where amplitude, frequency and starting phase define net result.
What is a sine wave?
Rotating phase in 360 degrees; oscillation in a circular fashion. How fast sine wave spins = phase.
Sound waves = sinusoids.
Sinusoids: What is frequency?
Number of complete cycles that occur in one second. Commonly used unit is Hz
Reciprocally related to period: f=1/P
Sinusoids: What is period?
Amount of time it takes to complete one full cycle (seconds)
P=1/f
What is starting phase?
Point in the displacement cycle the object begins to vibrate. Can have difference degrees as start phase
What is instantaneous phase?
Start phase both equal 0 degrees but phase at different points in time (instantaneous phase) differs between two waves
At certain time, where they intersect.
Look at which degree wave is sitting on.
What is amplitude?
Instantaneous amplitude?
Peak amplitude?
Measure of displacement. Measure of displacement of sine wave that varies with time - instantaneous amplitude.
Measure of displacement of a sine wave that doesn’t vary with time - peak amplitude, and RMS (energy in sinusoid)
What are the downfalls of peak amplitude?
Works well for sinusoids, insufficient for describing amplitudes of different frequency sinusoids over a specific interval; amplitudes of non-sinusoidal/complex waveforms
What is an FFT? Why is it important?
Samples signal over period of time and divides it into its frequency components. Components are single sinusoid oscillations at distinct frequencies each with own amplitude and phase.
What is Fourier’s Analysis?
Of a complex waveform expressed as a series of sinusoidal functions, the frequencies of which form a harmonic series. Difference shapes of time waveforms can be created by varying the relative amplitudes of the summed sinusoids.
What are two ways to represent a sound?
Time-domain and frequency-domain amplitude spectrum
How is sound a change of pressure in air?
4 Reasons
Waveform of any sound shows how the pressure changes over time
Eardrum moves in response to changes in pressure
Any waveform shape can be produced by adding together sine wave of appropriate frequencies, amplitudes and phases
Amplitudes of sine waves give the amplitude spectrum of the sound. For a sine wave this is a single point at the frequency of the sine wave.
