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What is simple harmonic motion?
- Equilibrium
- Maximum displacement in one direction
- Equilibrium
- Maximum displacement in the opposite direction
- Equilibrium
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What is Hooke's law?
- Magnitude of restoring force is proportional to distance displaced
- Fr is directly proportional to X
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Does the magnitude of restoring force change over time?
Yes. Kinetic energy changes to thermal energy because of friction. If X changes, Fr must change
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What is friction?
An opposition to motion
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How many frequencies is a sine wave?
- one
- speech is many frequencies
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What is on the x and y axis of a waveform?
- time is on the x axis
- amplitude is on the y axis
- amplitude can be anything (displacement, velocity, acceleration, force, pressure, momentum, etc)
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What is a waveform?
- a plot of change in amplitude (loudness) of displacement over time
- amplitude vs. time
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What is uniform circular motion?
- a point moves about the circumference of a circle at a constant number of degrees of rotation per second
- the point engages in SHM
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One cycle of uniform circular motion is equal to how many degrees?
360 degrees
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Is the motion of a spring-mass system circular?
No, it's rectilinear
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Which direction does uniform circular motion move?
- counterclockwise
- 90 degrees = max displacement
- 270 degrees = max displacement
- 0, 180, and 360 degrees = equilibrium
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What is sinusoidal motion?
- same as simple harmonic motion
- projection of sinusoidal motion is called a sine wave, or sinusoidal wave
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What are the 5 dimensions of sine waves?
- amplitude
- frequency
- period
- phase
- wavelength
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What is a phase?
where in time the wave begins (0, 90, 180, 270, or 360 degrees)
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What is amplitude?
- sound pressure
- directly proportional to force
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What is the starting phase of a sine wave?
it can be anything
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What are the phasic relations?
- displacement
- velocity
- acceleration
- pressure
- these relationships are always the same
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What would two waves starting at 0 degrees be considered?
in phase
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What is the relationship between particle velocity starting at 90 degrees and particle displacement starting at 0 degrees?
particle velocity leads particle displacement by 90 degrees
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Particle velocity leads particle displacement by 90 degrees. Why?
velocity is maximal at equilibrium where X is at zero; velocity is zero at Xmax where motion is momentarily halted
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How much does particle acceleration lead particle displacement by?
180 degrees
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What happens if two waves are 180 degrees out of phase?
they cancel each other out
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What are the starting phases of displacement, velocity, acceleration and sound pressure?
- displacement = 0 degrees
- velocity = 90 degrees
- acceleration = 180 degrees
- sound pressure = 90 degrees
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What is instantaneous amplitude?
- amplitude at a moment of time
- infinite amounts on a sine wave
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What is maximum amplitude?
amplitude from equilibrium to the highest possible peak
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What is peak-to-peak amplitude?
- amplitude from the highest point to the lowest point
- peak-to-valley
- have to take absolute value (2 and -2 = 4)
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What is amplitude measured in?
- voltage
- pascals
- decibels (dB)
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What is frequency?
- cycles per second (cps)
- measured in Hertz (Hz)
- inverse of period
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What is period?
- seconds per cycle (spc)
- the time required to complete one cycle
- inverse of frequency
- measured in seconds (s)
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How do you get from ms to s?
divide by 1000
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How do you get from s to ms?
multiply by 1000
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How do you get from Hz to kHz?
divide by 1000
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How do you get from kHz to Hz?
multiply by 1000
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What does frequency depend on?
- properties of the source of sound
- spring-mass system: mass and stiffness of system
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What does more mass mean?
lower frequency (male voice)
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What does stiffer mean?
- higher frequency
- vocal folds stretched apart (norah jones- stiff vs. rihanna- not stiff)
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What is natural frequency?
- the frequency with which a system oscillates freely (fnat)
- fnat = square root of s/m
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What are the proportional relations of fnat with s and m?
- fnat is directly proportional to square root of s- frequency increases as stiffness increases
- fnat is directly proportional to 1/square root of m- frequency decreases as mass increases
*frequency review page 26
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What is wavelength?
the space occupied by a complete cycle
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Do men or women have greater wavelength?
men
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What quantities are measured in wavelength with respect to time?
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What are the proportional relations of wavelength with speed of sound and frenquency?
- wavelength is directly proportional to speed of sound
- wavelength is directly proportional to 1/f
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What is damping?
an opposition to motion (friction or frictional resistance)
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What does friction limit?
velocity
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What is the relationship between velocity and damping?
directly proportional
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How much does momentum lead elasticity by?
90 degrees
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What is the relationship between displacement and elasticity?
in phase
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By how much does acceleration lead velocity and displacement?
- velocity- 90 degrees
- displacement- 180 degrees
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*Wavelength review page 29
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What causes damping?
as velocity increases, kinetic energy is transformed to thermal energy (friction)
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What is damping in phase with?
- velocity
- it varies over time
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What does magnitude of displacement depend on?
force applied
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What are the 3 types of damping systems?
- a lossless system
- low-damped system (vocal folds)
- high-damped system (ipod)
*page 30 slide 67
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What would happen if shock absorbers and VU meters where nearly undamped?
the sound would go on forever (excessive oscillation/vibration)
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What is impedance?
an opposition to motion
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What is the relationship between mass and frequency?
as mass goes up, frequency goes down
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What are the two components of total impedance?
resistance (R) and reactance (X)
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What is resistance?
- friction
- use up energy (kinetic energy is transformed to thermal energy)
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What is reactance?
- storage of energy as potential energy
- the amount of energy stored depends on the frequency
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What are the two types of reactiance?
- mass reactance (Xm)
- compliant reactance (Xc)
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Are resistance and reactance independent or dependent of frequency?
- resistance is independent of frequency (it doesn't matter what the freq. is)
- reactance is frequency dependent
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What is resistance measured in?
ohms
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*Reactance and phasic relations page 31
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What is the relationship between mass reactance and compliant reactance?
- when one reactance component stores energy, the other gives up energy
- they are 180 degrees out of phase
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What is mass reactance measured in and directly proportional to?
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What is the difference between mass reactance at low frequencies and high frequencies?
- low = negligible (small), larger amplitude of vibration
- high = large, smaller amplitude of vibration
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What is compliant reactance measured in and inversely proportional to?
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What is the difference between compliant reactance at low frequencies and high frequencies?
- low = large, smaller amplitude of vibration
- high = negligible, larger amplitude of vibration
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If frequency is less than natural frequency...
- impedance increases
- amplitude of vibration decreases
- compliance dominant
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If frequency is greater than natural frequency...
- impedance increases
- amplitude of vibration decreases
- mass dominant
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When is the amplitude of a wave the greatest?
- at natural frequency
- mass and compliant reactance cancel each other out (18- degrees out of phase)
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What are the phases of resistance and reactance?
- mass reactance leads resistance by 90 degrees
- compliant reactance leads resistance by 90 degrees
- mass reactance leads compliant reactance by 180 degrees
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