Transcript PHYSICAL CONCEPTS - University of Florida

CHAPTER 2
SINUSOIDS: THE BASIC SOUND
Hearing Science-- what is it?
• The study of the normal process of hearing.
Acoustics--the nature of sound
Anatomy & Physiology of the Ear
Psychoacoustics
Defining SOUND
• Psychological definition: Sound is a
stimulus with the capability of producing an
audible sensation.
• Physical definition: Energy produced by an
object in vibration and transmitted through
a medium.
VIBRATION
• vibration is the movement of an object from
one point in space to another, and usually
back to the first point.
• Objects that can be set into vibration have
two properties:
– elasticity
– inertia (fundamental feature of mass)
Elasticity is:
• The property that allows an object or substance
to return to its initial shape or state when it is
deformed, distorted or displaced.
Tuning fork: stiffness provides restoring force
Swing: gravity provides restoring force
Quantities Come in 2 Flavors:
• Scalar Quantities
– magnitude only
• Vectorial or Vector Quantities
– magnitude AND direction
Scalar Quantities
• Have magnitude only
• Examples include Mass, Length,
Volume
• Can be added or subtracted directly
Vector Quantities
• Have BOTH magnitude and
direction
• Example: Velocity
• Combining Vectors is more
complicated
Basic Units
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•
•
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Length
Time
Mass
(Charge)
Other Units may be
derived:
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•
•
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Area = Length x Length (or L2)
Volume = L3
Speed = Length/Time
Acceleration = L/T2
Force: A push or a pull
• Force = Acceleration x mass
• Therefore Force = ML/T2
• MKS force unit is Newton = 1 kg
m/s2
• cgs unit is dyne = 1 g cm/s2
Force and Elasticity
• Hooke’s Law:
• Force = (-)spring constant times displacement
• Stress = force per unit area (aka pressure)
• Strain = change in length
• Stress = Elasticity x Strain
Friction
• Energy converted into heat when molecules
rub against each other.
• To move an object, the applied force must
overcome friction.
• Effect of Friction is “Resistance”
Friction produces Resistance
• Resistance = ratio of Force to resulting velocity
(R = f/v)
• measured in Ohms
• Acoustically, we talk about the influence of
friction as DAMPING
Energy & Related Concepts
• WORK
• POTENTIAL AND KINETIC ENERGY
• POWER
WORK
• Force applied through a distance
• No motion--no work
• Work = force x distance = ML/T2 x L
• Units JOULE = 1 Newton Meter
•
erg = 1 dyne cm
ENERGY COMES IN 2 FLAVORS
• Kinetic-- Energy of motion
• (Inertia can be thought of as the ability to
store kinetic energy)
• Potential--Energy of position
• (Elasticity --ability to store potential
energy)
POWER
• Rate at which work is done
• Work/Time
• Unit Watt = joule/second or 107 erg/sec
SIMPLE HARMONIC MOTION
• Vibration involves interplay of force,
inertia, elasticity, and friction
• Applying a force displaces object
• Overcoming inertia
• Traveling away from rest until ?
Simple Harmonic Motion 2
• Why does object stop and then move back
toward rest?
• Why doesn’t the object then stop at rest?
• Where is potential energy the greatest?
• Where is kinetic energy the greatest?
SHM 3
• Why does displacement decrease over time?
• RESISTANCE
• -- Energy is lost to HEAT through
FRICTION
SHM 4
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Amplitude --Displacement
Period-- Time taken to complete one cycle
Frequency--Number of Cycles per Second
Phase--Describing points in the Cycle
A Waveform Shows Amplitude as
a Function of Time
DISPLACEMENT
1
PEAK
PEAK-TO-PEAK
0.5
0
-0.5
-1
-1.5
TIME
Period and Frequency
• Frequency = 1/Period (in seconds)
• Units of Frequency = cycles per second or
HERTZ
PHASE--Each cycle broken up
into 360 degrees
• 0 degrees = 0 displacement and about to
head positively
• 90 degrees = positive maximum
• 180 degrees=0 disp. About to head
negatively
• 270 degrees= negative maximum
Phase Values Through a Cycle
Displacement
90
1.5
1
0.5
0
-0.5
-1
-1.5
1/1/00
180
2/1/00
270
360
3/1/00
Time
4/1/00
AMPLITUDE MEASURES
• Instantaneous- amplitude at any given
instant
• Peak
• Peak to Peak
• Root Mean Square--A way of getting
average amplitude
• =Square root of Averaged Squared
Amplitudes
FREE VIBRATION
• Pendulum illustration represents FREE
VIBRATION
• Force applied and object allowed to respond
• Frequency of Free Vibration =Resonant or
Natural Freq.
• --determined by the object’s Mass and
Stiffness
FORCED VIBRATION
• Force is applied back and forth
• Vibration occurs at the frequency of the
applied force
• Object’s mass and stiffness determine
amplitude of vibration