Acoustics Ch. 1
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What is acoustics?
the study of sound
What is sound?
the movement of a disturbance (vibration) through a medium (air, water, etc)
What two properties must a source have to vibrate?
What is mass?
the amount of matter something has
What is elasticity?
the ability of something to return to its original shape
What two properties must a medium have to be capable of being set into vibration?
What is weight?
an attractive gravitational force
What is the relationship between mass and weight?
- they are directly proportional to each other
- air has mass AND weight
What is density?
- the mass per unit volume
- density = mass / volume
What is the concept of "elastic limit"?
if the shape or volume of something is distorted too much, the object will not be able to recover (breaking a rubberband)
What is the vibratory motion of a tuning fork?
- strike the fork: vibration occurs
- tines dispaced from equilibrium
- amplitude of displacement is proportional to force applied
What is inertia?
an object in motion stays in motion
What is the relationship between mass and inertia?
they are directly proportional to each other
Why does vibratory motion occur?
- the interaciton of two opposing forces: inertia and elasticity
- back and forth movement
What is the law of reaction forces?
- with every force there must be an equal and opposite reaction force (force cannot exist alone)
- vibration: elasticity is the reaction force to inertia (vibration continues without reapplication of external force- vibration sustained by opposing forces)
What two opposing forces cause particles to move about positions of equilibrium?
What is compression?
- maximum displacement in one direction
- density increases
What is rarefaction?
- maximum displacement in the opposite direction
- density decreases
What is propagation?
alternations between increased density (compression) and decreased density (rarefaction)
What are the three fundamental physical quantities?
- *derived physical quantities are based off of these
What are the MKS measures for length, mass, and time?
- length = m
- mass = kg
- time = s
What is length?
the amount of spatial separation between two points
What are the conversions from 1 in, 1 ft, 1 m, 1 cm, and 1 mm?
- 1 in = 2.54 cm
- 1 ft = .3048 m
- 1 m = 100 cm
- 1 cm = .01 m
- 1 mm = .001 m
A steel ball and ping-pong ball are the same size: which as greater mass, hence greater inertia?
the steel ball
What is time?
a quantity expressed in seconds (s), minutes (min), hours (hr), etc
What is a derived quantity?
- a quotient or product of fundamental, or of fundamental and derived, physical quantities
- ex. area (length x width)
What are the derived quantities?
- displacement (x)
- velocity (c)
- acceleration (a)
- force (F)
- *pressure (p)- ear drum moves based on pressure from compression and rarefaction
What is displacement?
- a vector quantity that incorporates both magnitude and direction
- it is directly proportional to the applied force
- (*page 8, slide 33)
What is velocity?
the amount of displacement per unit time (how quickly dispacement takes place in m/s)
What is acceleration?
- the time-rate change in velocity
- has to do with not going same speed and direction in every unit time (making a turn = change in direction = acceleration)
- vector quantity
What is the difference between positive and negative acceleration?
- positive = accelerating
- negative = decelerating
What is the equation for acceleration (a)?
a = change in c/t = (c2-c1)/t
c1 = 20 m/s
c2 = 40 m/s
t = 5 s
What is a?
a = (40-20)/5 = 4 m/s/s = 4 m/s^2
A car moves around a circular tract at a constant speed. Is it accelerating?
Yes! Direction is changing, hence velocity is changing. Velocity cannot change without acceleration.
What is force?
- a push or pull
- the product of mass and acceleration (F = ma)
What are the consequences of a force?
- distortion of matter (changing shape)
- acceleration of matter
What is force measured in?
What is pressure?
- force per unit area (p = F/A)
- measuring p = measuring compressions and rarefactions
What are the units of measure of pressure?
N/m^2 = pascal (Pa)
How does the vibratory motion of a spring-mass system work?
spring is at equilibrium, spring is compressed causing maximum displacement in one direction, elasticity returns it to equilibrium, spring is stretched causing maximum displacement in the opposite direction, elasticity returns it to equilibrium
What is the restoring force of a spring-mass system?
What is Hooke's law?
- magnitude of restoring force (elasticity) is directly proportional to magnitude of displacement
- Fr = -kx
- Fr = restoring force
- -k = a constant (stiffness or compliance- how is it is or is not to displace something)
- x = displacement
- *if k is small, easy to displace and vice versa
What two opposing forces allow vibration to be sustained in a spring-mass system?
What is the restoring force of a pendulum?
What are the 2 opposing forces of a pendulum?
How do the inertial and restoring forces work in a pendulum?
- inertial force (movement) is maximal at equilibrium and zero at maximum displacement where motion is momentarily halted
- restoring force (gravity) is maximal at maximum displacement and zero at equilibrium
- *inertia makes it move past equilibrium
- *gravity pulls it back to equilibrium
Why does pendulum gain momentum as it approaches equilibrium?
- because velocity increases (M = mc)
- *as velocity increases, momentum increases
How do velocity and momentum work in a pendulum?
- velocity is maximal at equilibrium and zero at maximum displacement where motion is momentarily halted
- momentum is also maximal at equilibrium and zero at maximum displacement where motion is momentarily halted
What is the energy principle?
- used to describe vibratory motion of a pendulum
- system must receive a supply of energy or nothing will happen
What can energy produce a change in?
matter (displacement, distortion)
What is kinetic energy?
- energy of movement
- as you reach maximum displacement you use up kinetic energy
What is potential energy?
What is energy?
- the capacity to do work (make matter change)
- if a change in matter occurs, work has been done
What is the difference between energy and work?
- energy is something that a body possesseswork is something that a body does
What is the equation for work?
W = Fd (work = force x distance)
What is the unit of measure for work?
What is the transformation of energy?
energy is not depleted; it is transferred or transformed into potential or kinetic energy
When is kinetic energy maximal and zero in a pendulum?
- maximal lat equilibrium where velocity is maximal
- zero at maximum displacement where motion is momentarily halted and velocity is zero
Where is potential energy maximal and zero in a pendulum?
- maximal at maximum displacement
- zero at equilibrium
What is frictional resistance?
- a force that opposes motion and thus limits velocity
- motion ultimately ceases because of frictional resistance
What is kinetic energy transformed into and what does this result in?
- thermal energy (heat) because of friction
- it results in damping because energy is lost and vibration stops
What are the characteristics or pendular motion?
- amplitude (how much) of displacement (change in distance)
- frequency (f)
- period (T)
What is frequency?
- the rate of vibratory motion
- the number of cycles per second (cps)- one cycle = simple harmonic motion
What is the unit of measurement for frequency?
What defines "one cycle"?
movement from equilibrium to maximum displacement in one direction, back to equilibrium, on to maximum displacement in the opposite direction, and then back to equilibrium
What is period?
- the time required to complete one cycle (goes hand in hand with frequency)
- T = 1/f
- f = 1/T
How does sound wave propagation work?
- one cycle causes other air molecules to begin cycles
- *cork moves up and down, but waves move all the way across water
How does the rate of vibratory movement compare to the rate of wave propagation?
- the rate (frequency) of vibratory movement is how fast vocal cords are moving
- the rate (speed) or wave propagation is how fast compressions and rarefactions (created by source) move through the air
- *affected by mediums (air, water, etc)
How is the frequency of vibratory motion determined?
- frequency of vibration of the source is determined by characteristics of the source (density, length, etc)
- frequency of vibration of air particles is the same as frequency of the source (air particles move as fast as vocal folds)
What is the speed of wave propagation governed by?
properties of the medium
What is the speed of sound through air?
331 m/s or 1086 ft/s
What are the two types of wave motion?
- transverse- particle moves perpendicular to propagation
- longitudinal- mass and propagation of wave move in same direction (*sound waves are longitudinal)
- *page 17, slides 89 and 90
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