Acoustics Ch. 2
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What is simple harmonic motion?
 Equilibrium
 Maximum displacement in one direction
 Equilibrium
 Maximum displacement in the opposite direction
 Equilibrium

What is Hooke's law?
 Magnitude of restoring force is proportional to distance displaced
 Fr is directly proportional to X

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

What is friction?
An opposition to motion

How many frequencies is a sine wave?
 one
 speech is many frequencies

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)

What is a waveform?
 a plot of change in amplitude (loudness) of displacement over time
 amplitude vs. time

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

One cycle of uniform circular motion is equal to how many degrees?
360 degrees

Is the motion of a springmass system circular?
No, it's rectilinear

Which direction does uniform circular motion move?
 counterclockwise
 90 degrees = max displacement
 270 degrees = max displacement
 0, 180, and 360 degrees = equilibrium

What is sinusoidal motion?
 same as simple harmonic motion
 projection of sinusoidal motion is called a sine wave, or sinusoidal wave

What are the 5 dimensions of sine waves?
 amplitude
 frequency
 period
 phase
 wavelength

What is a phase?
where in time the wave begins (0, 90, 180, 270, or 360 degrees)

What is amplitude?
 sound pressure
 directly proportional to force

What is the starting phase of a sine wave?
it can be anything

What are the phasic relations?
 displacement
 velocity
 acceleration
 pressure
 these relationships are always the same

What would two waves starting at 0 degrees be considered?
in phase

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

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

How much does particle acceleration lead particle displacement by?
180 degrees

What happens if two waves are 180 degrees out of phase?
they cancel each other out

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

What is instantaneous amplitude?
 amplitude at a moment of time
 infinite amounts on a sine wave

What is maximum amplitude?
amplitude from equilibrium to the highest possible peak

What is peaktopeak amplitude?
 amplitude from the highest point to the lowest point
 peaktovalley
 have to take absolute value (2 and 2 = 4)

What is amplitude measured in?
 voltage
 pascals
 decibels (dB)

What is frequency?
 cycles per second (cps)
 measured in Hertz (Hz)
 inverse of period

What is period?
 seconds per cycle (spc)
 the time required to complete one cycle
 inverse of frequency
 measured in seconds (s)

How do you get from ms to s?
divide by 1000

How do you get from s to ms?
multiply by 1000

How do you get from Hz to kHz?
divide by 1000

How do you get from kHz to Hz?
multiply by 1000

What does frequency depend on?
 properties of the source of sound
 springmass system: mass and stiffness of system

What does more mass mean?
lower frequency (male voice)

What does stiffer mean?
 higher frequency
 vocal folds stretched apart (norah jones stiff vs. rihanna not stiff)

What is natural frequency?
 the frequency with which a system oscillates freely (f_{nat})
 f_{nat }= square root of s/m

What are the proportional relations of f_{nat} with s and m?
 f_{nat} is directly proportional to square root of s frequency increases as stiffness increases
 f_{nat} is directly proportional to 1/square root of m frequency decreases as mass increases
*frequency review page 26


What is wavelength?
the space occupied by a complete cycle

Do men or women have greater wavelength?
men

What quantities are measured in wavelength with respect to time?

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


What is damping?
an opposition to motion (friction or frictional resistance)

What does friction limit?
velocity

What is the relationship between velocity and damping?
directly proportional

How much does momentum lead elasticity by?
90 degrees

What is the relationship between displacement and elasticity?
in phase

By how much does acceleration lead velocity and displacement?
 velocity 90 degrees
 displacement 180 degrees

*Wavelength review page 29

What causes damping?
as velocity increases, kinetic energy is transformed to thermal energy (friction)

What is damping in phase with?
 velocity
 it varies over time

What does magnitude of displacement depend on?
force applied

What are the 3 types of damping systems?
 a lossless system
 lowdamped system (vocal folds)
 highdamped system (ipod)
*page 30 slide 67

What would happen if shock absorbers and VU meters where nearly undamped?
the sound would go on forever (excessive oscillation/vibration)

What is impedance?
an opposition to motion

What is the relationship between mass and frequency?
as mass goes up, frequency goes down

What are the two components of total impedance?
resistance (R) and reactance (X)

What is resistance?
 friction
 use up energy (kinetic energy is transformed to thermal energy)

What is reactance?
 storage of energy as potential energy
 the amount of energy stored depends on the frequency

What are the two types of reactiance?
 mass reactance (Xm)
 compliant reactance (Xc)

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

What is resistance measured in?
ohms

*Reactance and phasic relations page 31

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

What is mass reactance measured in and directly proportional to?

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

What is compliant reactance measured in and inversely proportional to?

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

If frequency is less than natural frequency...
 impedance increases
 amplitude of vibration decreases
 compliance dominant

If frequency is greater than natural frequency...
 impedance increases
 amplitude of vibration decreases
 mass dominant

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)

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