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# Hearing Science 1

### Exam 1: Durrant & Feth, Ch.2&3 - Physics and Applied Acoustics, Measurement of S

Δ delta - change
Σ Sigma - Sum of #s
σ sigma - standard deviation
θ theta - threshold
λ lamda - wavelength
π pi - 3.1415
1 kg expressed in grams 10^3 g
1 m in centimetesr 10^2 cm
1 cm in meters 10^-2 m
1 mm in meters 10^-3 m
1 microsecond (μs) expressed in seconds 10^-6 seconds (micro = "millionths")
1 millisecond (ms) expressed in seconds 10^-3 seconds (milli = "thousandths")
What are Derived Quantities? Any combination of mass, length, & time
What are Scalar Quantities? Magnitude only --> Ex) Length, Speed
What are Vector Quantities Magnitude + Direction Ex) Displacement, force, acceleration, velocity
1 g expressed in kg 10^-3 kg
What is Average Velocity? Equation? Units of measure? the time-rate change in displacement
What is Acceleration? Equation? Units of measure? the time-rate change of Velocity (the fluctuations or instant-to-instant changes in Velocity)
When Velocity is truly constant, the acceleration is_____? zero (even if the velocity is not equal to zero [in other words, the object is not at rest])
What is Vibratory Motion? Occurs at a fixed point as an object moves back and forth. It can also be defined as an object forced to move to and fro periodically, occurring when a particle is vibrated. Oscillatory motion is related to vibratory motion.
What does Simple Harmonic Motion (SHM) represent? The most basic form of vibratory motion --> The cyclic (alternating) exchange of kinetic & potential energy -Repetitive back & forth changes in direction, like the swinging of a pendulum
What is the Equation for Velocity? Units of Measure? - Average v = Change in displacement / change in time -Meters/second or km/second or cm/second
What is the Equation for Acceleration? Units of Measure? - Acceleration = Change in Velocity / time - m/s^2 or cm/s^2
What is a Simples Harmonic Oscillator (SHO)? How is it started? The name for a Simple Spring-Mass System when used to produce Simple Harmonic Motion -Is started with Force: a push (compressing the spring) or pull (extending the spring)
When is the mass in a SHO resting at equilibrium? When the spring is neither compressed nor extended (no force has been applied to the system): There is no motion, consequently
What is Force? Units of Measure? A push or pull. The rate of change of momentum F = ma 1 Newton: Force required to accelerate a body whose mass is 1 kg at a rate of 1 m/s^2 1 dyne = 1 g at a rate of 1cm/s^2
What do the first 2 of Newton's Laws express? In essence, the idea that a force is required to change the motion of an object, whether the change is from zero velocity (an object at rest) to any magnitude of velocity or a change in the existing motion (an object speeding up).
What is inertia? A body tends to oppose any change in motion -One of the 2 properties that keep the mass vibrating in the simple spring-mass system once it is stated -AKA: The ability of an object to store kinetic energy
Describe the motion of the mass in SHM Constantly changing
What quantities are constantly changes in SHM? Velocity, Acceleration, and Displacement
What does Newton's Second Law state? That the Force involved in the motion of an object is determined by just two factors: Its Acceleration & its Mass. Specifically, Force is the product of mass & acceleration F = ma
If there is no change in motion (if acceleration = 0), then... (this is AKA...) Force is zero. Specifically, Net Force acting on an object is 0. "Equilibrium"/ "resting state"
When forces of unequal magnitude & different directions are acting on an object, the object will: Move in the direction of the greater force, with acceleration proportional to the net force acting on it. On the contrary, forces acting in the same direction will add
Momentum is: The product of mass and velocity. Force is the rate of change of momentum.
Describe Velocity in SHM Velocity peaks as the mass heads back toward E - So the mass keeps moving. It then started to lose its momentum, coming to a halt at -A (suspended in a balance/neutralization of forces, at least for an instant). Implies another force acting in the SHO.
What is Elasticity? The physical property by which an object deformed in shape, size, or length by an applied force, within the limits of elasticity, returns to its original shape when the applied force is removed. AKA: The ability of a substance to store potential energy.
What is a Restoring Force? A force developed in opposition to displacement (when a spring pushes or pulls back in response to the other)
What is Stiffness? The degree of restoring force developed for a given change in length, size, or shape. The stiffer a spring, the more force is required to extend or compress it.
What is Hooke's Law? The expressed relationship among restoring force, stiffness, and amount of deformation or displacement (such as change in length). F = -kx Where k is the spring constant, a measure of stiffness
The (-) in (-k) indicates: That the restoring force opposes the applied force
Compliance is ____. the reciprocal of Stiffness. A more compliant spring is less stiff (that is, has more "give"), and vice versa.
The more compliant the spring, the ______. less force required to displace it.
Compliance is measured in units of m/N
The vibratory motion of the simple SMS, initiated from a simple push or pull, must be attributed to what interaction? The interaction between the inertia of the mass and the stiffness of the spring as it is alternately compressed & extended upon displacement of the mass.
In an idealized system, the motion of mass in a SMS: Retraces itself endlessly
In terms of simpler motion (than SHM), what is steady-state motion? The achievement of a constant velocity after a certain amount of acceleration... Which happens b/c the applied force will then be balanced by frictional force.
If Friction were not present, Even the smallest continuous force applied to the object would cause it to accelerate indefinitely
If the frictional opposition, or resistance, is overcome with increased force... the object is again accelerated.
The opposing force of friction is: velocity-dependent: friction limits velocity.
The coefficient of friction depends on 3 main concepts: 1) both the nature of the surfaces 2) The force holding the surfaces together. Example of Force = Weight (gravity acting on the mass of an object) 3) Whether the object is in motion or at rest
What is viscosity? What does it do? Fluid friction - Imparts damping to vibratory systems Ex) The shocks in the suspension systems of automobiles employ viscous damping
Give and explain the components of the mathematical formula for Friction F=-rv r is mechanical resistance in the system (measured in terms of force per unit velocity [1 N/m/s in MKS units = 1 Ohm])
How quickly motion diminishes depends on the amount of damping
What is Critical damping? A mass comes to rest as quickly as possible (in barely 1 alternation/cycle of the motion) after initial displacement and release
What is the name for the effect of the stereotypical rate of decay of damped vibration? Exponential Decay -Multiplies the Sine function
What is Work? How is work mathematically expressed? Force of an object acting through some distance. W = F × d
The Law of Conservation of Energy states that ____. Energy can be transformed from one form to another, but cannot be destroyed
Potential Energy Energy that was "utilized" now must be available to do work once more
A deformed substance has ____ ____ by virtue of its elasticity, since work was done in deforming the substance, which required a force to act through a certain displacement. potential energy
When the applied force is removed, the ____ ___ is available to do work. Restoring force
Kinetic Energy is: A property of an object in motion -When the mass in the SHO was released, the energy stored in the spring was converted gradually to kinetic, and the mass began to vibrate
What are the units of measure of Work and Energy? The unit of Energy: A force of 1 Newton acting through a distance of one meter (a "Joule") 1 Dyne acting through a distance of one centimeter (an "Erg")
Friction's influence: Dissipation of Energy (Friction transforms energy [from mechanical to heat, for example]) and Demise of Perpetual Motion
Energy is stored by virtue of ____ and ___. Elasticity, mass
Some damping, and thus energy dissipation, are _____ in the real world. inevitable
What is Power? (2 Definitions) 1) The rate at which work is done, or, the rate at which energy is expended. 2) The product of Force & Velocity.
How is Power measured? mathematically expressed? The Watt, for both CGS & MKS. 1 Watt = 1 Joule/s = 10 Ergs. Power = Δ W / Δ t
More power is required to increase either ___ or ____ in a given situation Force, velocity
Upon starting the Simple SMS or SHO, the mass is _______. displaced by some distance +A - E = A since by definition the displacement at E (equilibrium) is zero.
In SHO, Amplitude is: The peak value.... AKA: The displacement by some distance +A - E = A since by definition the displacement at E (equilibrium) is zero. Amplitude is the greatest value of displacement from the motion that ensues upon release of the mass
Peak Amplitude is: The distance between +A and -A
A displacement Waveform is: The name for the shape of a sequence of magnitudes along a particular function of time
What is Damping? Amplitude diminishing as time goes on
What are Cycles? The apparent intervals of alternation of motion -The interval of time between crossings of the zero axis in the same direction. -Are not impacted by the manner in which the SHO was started
How are Cycles/Periods measured? expressed? Measuring the time between successive peaks on the same side of the zero axis T = 1/f
Frequency is ___ related to Period inversely .... (Frequency & Period are reciprocals)
What is Frequency? How is it expressed & measured? f= 1/T The number of periods, or cycles, completed per unit time --> Cycles per second (cps). Hertz (Hz) ... kilo & mega are two common metric multipliers
longer T, lower f An oscillation with relatively longer periods has a relatively lower frequency. Similarly, shorter-period oscillations have higher frequencies.
Within certain limits, Frequency (or period) is completely independent of _____. Amplitude
If something is observed to have a fundamental period of repetition of the given motion, it is said to be _____. periodic, or to have periodicity Ex) SHO
The Fundamental Frequency is the _________ of the fundamental period. reciprocal
Phase is a value that _____ throughout the cycle. changes
Phase is used to: Specify a particular reference point within the cycle
Phase is expressed in: Degrees or Radians, units of measure from trigonometry wherein the cycle comes full-circle in 360 degrees or 2π radians -p.38 figure = motion initiated at 90 degrees
One-quarter cycle = The excursion from __ to __. E, +A
In Sinusoidal Motion, the second half of the total amplitude (so, after the first half of the amplitude) consumes ____ __ __ __ __ __. more than twice as much time. (The mass must slow down, and then completely stop for an instance, in order to reverse motion)
The mass is not moving in a circle; it is the __ __ that is "circular," conceptually. time course
The movement of a point around a circle when plotted over all phases of the cycle defines the ___ __. Sine Wave
θ = The sine of the phase, or the Phase angle
sin(θ ) The sine of the phase of the phasor = x/r (x = instantaneous displacement)
2π radians = 360 degrees, Circumference of a circle
___ is the function/dependent variable being evaluated against each instant in time, t, the independent variable x(t)
In SHM, the value of the sine itself ranges from __ to __. The value of the function (x(t)) varies between __ to __. -1, 1 +A, -A
__ __ is a parameter that may be the only distinction between two vibrations that are otherwise identical in waveform Starting Phase
Velocity is said to ____ displacement. lead
Acceleration is ___ when velocity is zero greatest p.51
Acceleration is said to ____ velocity (and displacement). lead
Displacement lags ___ velocity
Velocity lags ___. acceleration
Natural frequency = System vibrating naturally at one frequency... Uniquely determined by the amounts (balance) of mass and stiffness in the system -No additional force required to keep the ideal or frictionless simple spring-mass system in vibration
The natural frequency is proportional to the ___ __ __ ___ and is inversely proportional to the __ __ __ ___. square root of stiffness, square root of mass. Ex) If stiffness is increased 4 times, the Nat. Freq. doubles. Ex) If mass is increased four times, the Nat. Freq. is halved.
A resonance curve shows us that: Something is vibrating at optimal frequency
The response of a system to applied vibration = __ __ Forced response
-The respective "reactions" of mass & stiffness act in __ ___ __ to each other, showing a phase difference of _ degrees direct phase opposition, 180
Both mass & stiffness are ___ out of phase with velocity. Why? 90 degrees. The opposition afforded by the mass in the system is proportional to acceleration (Newton's law) , whereas the restoring force is proportional to displacement (Hooke's law)
Stiffness Reactance (AKA: negative reactance) opposes vibration in __ frequencies low
Mass Reactance (AKA: positive reactance) opposes vibration in the ___ frequencies high
If you subtract Stiffness from Mass, and vice versa, they will cancel each other out and become zero at the center point, right where the resonant frequency is
Mass & Stiffness Reactance are ___ -dependent frequency
Condensation/Compression is an area of ____ ___ Rarefaction is an area of ____ ____. increased pressure/density, decreased pressure/density (relative to the pressure here on earth)
Ambient pressure: Atmospheric pressure
The opposite of resonance is ___ Impedance
Period is related to ____ frequency