Exam 1 Physics of Musical Sound
The larger the mass the
greater the force of gravity
inter-molecular forces
holds things together, created by electrostatic force. in water , hydrogen atoms, the electron is attracted to the oxygen
Definition of Work
if a force F is applied to an object (that moves distance (d) then W = Fd
Sensitivity to frequency
audible range for humans 20 Hz to 20,000 Hz. Humans are insensitive to low pitches. Infrasonic sounds below 20 Hz. Ultrasonic sounds above 20,000 Hz too high pitch for human ears
trough of transverse wave
bottom of wave
pinna
external ear; collects sound, protects ear, impedance transformer
Simple Pendulum
f depends on length of sting and acceleration due to gravity
Second overtone (third harmonic) (open pipe)
f frequency = 3v/2L = 3f1
First overtone (second harmonic) (open pipe)
f frequency = v/L = 2v/2L = 2f1
frequency
f. number of vibrations per second use Hz. 1/P
Fundamental Frequency (first harmonic): f1 (string)
f1 = v /λ= v /2L
Second Harmonic: f2 (string)
f2 = v/λ = v/L= 2f1
Third harmonic: f3(string)
f3 = v/λ = 3v/2L = 3f1
as the mass of an object increases
it accelerates under a force decreases . F=ma
Critical bands
frequency band within which two or more tines excite many of the same hair cells on the basilar membrane and thus are difficult to distinguish as separate tones. 24 spanning in the audible range.
The greater the distance the
less force due to gravity
sensitivity to loudness
minimum audible sound (MAS): 0 db softest sound we can hear. Pain: around 120 dB, or about 1 trillion (10^12) times the energy of MAS .
Pendulum converts
P.E. to K.E. and back to P.E; slows down and stops because friction, energy its losing.
Converting PE to KE and back to PE - Pendulum-At the top when it stops its
PE
Resonance
one objects vibrates at the natural frequency of a nearby object, and the second object vibrates violently,
Work is done against any force, until ____ slows it down. The work done by, or energy transferred by a force acting thru distance
friction
Properties of mechanical waves
require no medium, no net transfer of matter, speed of wave depends on medium, speed of sound: around 1100 ft/s in air, around 4800 ft/s in water
mechanical waves
requires a medium. water waves, seismic waves, sound
electromagnetic waves
requires no medium; light, heat, radio waves
Physical application for N masses on N + 1 springs
strings
vibrating string
strings only vibrate in transverse modes
All object falling under gravity, alone, no friction (free falling)
the acceleration is the same. 9.8 m/s^2 or 32 ft/ s^2.
Law of reflection
the angle at which a wave hits a surface is equal to the angle at which the wave bounces off the surface
Vibrating bar Case 1
the bar is loosely pinned at two points but not at ends; xylophone, chime bar, glockenspiel
when you speak or sing
the vibration must travel from a narrow opening (inside your throat and mouth) with higher impedance into the open air (lower impedance)
regular reflection
regular reflection off a smooth surface. notice that if the incident rays are parallel, so are the reflected rays. Regular reflection can produce an image.
types of reflection
regular reflection, diffuse reflection, and reflection off a smooth, parabolic wall
reverberation
when it comes back to fast within 0.1 s
harmonics
when the higher modes have frequencies that are whole # multiples of the fundamental frequency
How the inner ear works
when the stapes vibrates, the footplate pulls and pushes against the oval window making it vibrate
Acoustic reflex
when there is a loud noise it protects the ears. Tensor tympani muscles tightens the eardrum; eardrum moves away from the hammer; the stirrup moves away from the oval window. Delay time starts 30 ms to 40 ms after the sound starts
potential energy
when work is done against any force except friction, energy is stored as
nodes
points at which the particles remain at rest
antinodes
points of maximum motion
Second Harmonic: f2 (string)
λ = L (Two half-waves on the string)
nth harmonic: fn (string)
λn = 2L/n (Has n half-waves on the string)
Binaural hearing or low frequencies
1000 Hz or less. Low frequency sounds have a wavelength much larger than the distance between the two ears. Therefore, you can judge direction of a sound of low frequency by the phase difference between the sounds picked up by each ear
Air pressure
14.7 pounds per square inch. pressure that is put on your head.
Newton's 2nd Law - The fundamental law of physics F = ma to get a 1K kg car to accelerate at 0.5 m/s<2>, F = 1000 (0.05) = 50 N HEADS UP - MOVE DECIMAL OVER FOR SQ. INCHES.
- If an unbalanced force is applied to an object, it accelerates in the direction of the unbalanced force. - As the force on an object increases, the acceleration increases proportionally - As the mass of an object increases, its acceleration under a force decreases mathematically F = ma
Static electricity
- causes of intermolecular forces - protons and electrons arrange themselves and attract each other
The FLOW OF WATER gets thinner because like cars on a highway that pass through a narrower area, they must speed up to accommodate the speed of traffic. Now consider two points along the highway. At point one, the flow is proportional to the cross-section (A1) and the speed (v1) at that point. And at point two, the flow is proportional to the cross-section at point two (A2) and the speed at point two (v2). Since the same number of cars must pass both points, then A1 times v1 must equal A2 times v2 . Although some people do not appreciate mathematical expressions, this fact is probably best represented in that manner,
(A1) x (v1) = (A2) x (v2) . In fluid physics this equation is called the equation of continuity, which simply says "what flows in must equal what flows out." The water that emerges from the faucet is falling. What happens to any object that falls under the influence of gravity? It travels faster the further it falls (at least over short distances). From the above mathematical expression, one can understand that if we have a higher velocity (larger v2) at the bottom of the stream, then the cross-section (A2) is going to have to be smaller in order for the flow rate to remain the same. Thus the size of the stream (A2) gets smaller the further (and faster) the water falls. If the stream falls far enough, the water reaches a terminal speed and the size of the stream will stop decreasing in size or becoming smaller as it falls.
Subjective sound measurement
(perceived) loudness, pitch, and timbre (quality)
f=
1/T
Constructive interference
2 waves of equal frequency and phase produce a single amplitude equal to the sum of the amplitudes of the individual waves . f is the same
beats
2 waves of slightly different f produce periodic silence. the waves go in and out of phase, beats are destructive interference. the number of beats per second= the difference in frequency.
destructive interference
2 waves of the same f arrive at a point 180 degrees out of phase. frequency stays the same and the amplitude cancels (subtracts). examples speaking without a microphone
Air Pressure - Atmospheric pressure is the force per unit area exerted on a surface by the weight of air above that surface in the atmosphere of Earth. As elevation increases, there is less overlying atmospheric mass, so that atmospheric pressure decreases with increasing elevation. On average, a column of air one square centimeter in cross-section would have a weight of about 14.7 lbs, or about 65.4 N). Atmospheric pressure is sometimes called barometric pressure. So a 12" x 24" table has __ amount of pressure.
288 x 14.7Pa = 4,234 lbs. Air pressure from below the table is equal to the pressure above the table so it's balanced, and doesn't break. A 100 lbs. woman with 1/4 spike heels exerts how much pressure in psi (lbs. sq. inch)? P = F/A; PA = 14.7 (100 lbs./ 1/4 x 1/4) = 1600 psi
An object in free fall (no forces but gravity) near Earth: g =
32 ft./s<2> = 9.8 m<2>
An acceleration of 4 m/s<2> means your velocity increases
4 m/s each second
Binaural hearing for high frequencies
5000 Hz. For high frequencies, phase differences means nothing because the wavelength is less than the distance between your ears; you tell direction by the difference in loudness. Sound intensity drops off very quickly- as one over the distance squared) so if the sound comes from one direction the difference in loudness is noticeable. Also your head absorbs much of the sound, creating an "acoustic shadow" and helping this process. You cannot do this with low frequencies, since the sound diffracts a great deal.
T
= 1/f
v
= f/λ
If no forces are acting on an object, does it follow that the object is at rest? Explain.
According to Newton's First Law (aka Law of Inertia) "an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force". Consider a spacecraft traveling to the Moon. Once it has fired its rocket engines to leave Earth orbit, it will continue on that path and at that same speed without any need for further engine power. So it is moving, but without any force acting on it.
Are there forces on an object at rest?
An object being at rest can have forces acting on it however the vector sum of those forces, called net force, must be zero. This can easily be shown using Newton's Second Law. F(net) = m a, object at rest implies a = 0 so F(net) = m (0) = 0 Ex: a glass sitting on a table. The force of gravity (weight) is acting on the glass in a downward direction and a normal contact force from the table is acting on the glass in an upward direction. When you add these two forces together, you get zero net force, which means zero acceleration. Therefore, the glass at rest on a table will not move in this situation.
Hooke's law Mathematically F = -kx k = constant (stiffness)
As the force on a spring increases, the spring stretches proportionally
Vibrating plates
Chladni's method of sprinkling sand on a plate, drawing a bow against the edge to make it vibrate
When a piano is out of tune, you hear beats when you press one key. How can one note produce beats by itself?
Each note on a piano has 3 strings. If one of the strings are not tuned correctly, they will not all make the same sound to produce that particular note.
Newton's Third Law
For every action there is an equal and opposite reaction. Ex: rocket lifts off by ejecting gases out the back & force from ground pushes back
Acceleration forumula
Force/ Mass
Pressure
Force/Area = Newton/m<2> = Pascal At sea level, air pressure = 14.7 lbs/m<2> = Pascal
First overtone (third harmonic) (stopped pipe)
Frequency f = 3v/4L= 3f1 (the third harmonic)
Second overtone (fifth harmonic) (stopped pipe)
Frequency f = 5v/4L= 5f1 (the fifth harmonic)
First harmonic (fundamental f) (open pipe)
Frequency f1 = v/2L
First harmonic (fundamental f) (stopped pipe)
Frequency f1 = v/4L
What is meant by a "stiff spring"? Give your answer first in terms of forces, and then in terms of the spring constant k.
Hooke's law: As the force on a spring increases, the spring stretches proportionally Fspring = -k•x where Fspring is the force exerted upon the spring, x is the amount that the spring stretches relative to its relaxed position, and k is the proportionality constant, often referred to as the spring constant. A stiff spring would have a high spring constant - a relatively large amount of force to cause a little displacement. The units on the spring constant are Newton/meter (N/m). Positive if you're applying force Negative - if spring is applying the force.
Potential Energy
In physics, potential energy is the energy that an object has due to its position in a force field or that a system has due to the configuration of its parts. Common types include the gravitational potential energy of an object that depends on its vertical position and mass, the elastic potential energy of an extended spring, and the electric potential energy of a charge in an electric field. The SI unit for energy is the joule (symbol J).
A window is a rectangular plate of glass 2 m by 4 m. Find the total force exerted by air on this window when the air pressure is 1.013x10<5> Pa (1 atmosphere). Why does the window remain unbroken under this tremendous force?
It doesn't break because the same force is being exerted on the other side. Net force = 0
Converting PE to KE and back to PE - Pendulum-when it swings back down, it's ___
KE
First overtone (second harmonic) (open pipe)
L = λ (Length of the pipe is one wavelength)
Case N
N longitudinal modes, the mode in which all the masses move together is the symmetric mode; this has the lowest frequency, 2N transverse modes (N modes in - and - out of page, N modes up and down
Units: Joule =
Newton-meter
Force - push or pull expressed in ___ units
Newtons
Bernoulli Principle
The faster a fluid (liquid or gas) flows, the lower pressure it exerts.
Accleration
The rate of change of velocity. g = acceleration due to gravity. On Earth g = 32 ft/s<2> = 9.8m/s<2> t= 0 1 sec. 2 sec. 3 sec 0 mph 5 mph 10 mph 15mph
Newton's first law (AKA Law of Inertia)
The tendency of an object to keep doing what it's doing unless acted on by an external force. Depends on the mass of the object. Also, a passenger is unrestrained & the car crashes, the body is still in motion
A 60 W light bulb uses 60 Joules of energy per second. How much energy does it use in 1 hr? At what rate is work being done?
W = Pt = 60 (60) = 3600 seconds x 60 = 216,000 J so he multiplied time x
Power =
Work/Time the rate of doing work. It is equivalent to an amount of energy consumed per unit time. In the MKS system, the unit of power is the joule per second (J/s), known as the watt in honor of James Watt
Velocity
a rate of change of position (60m/hr) (not distance) means you cover 60 meters in an hour. You can drive in circles & cover 60 meters. The rate at which you're changing speed is going up meters per second
Newton's law of inertia (first law)
a body in motion tends to stay in the same motion, and a body at rest tends to stay at rest unless acted on by an unbalanced, external force.
Scala vestibule
a canal in the ear that transmits pressure variations from the oval window to the cochlear duct
Displacement
a change in position (in meters)
Ossicles lever action
a lever which changes the very small pressure exerted by a sound wave on the eardrum into a much greater pressure (up to 30 times) on the oval window of the inner ear. acts as a impedance transformer between the tympanic membrane and the oval window.
Reissner's membrane
a membrane in the cochlea that separates the cochlear duct from the scala vestibule
Eustachian tube
a tube connecting the middle ear to the oral cavity that allows the average pressure in the middle ear to equal atmospheric pressure
impedance mismatch
a wave tries to leave on material and enter another. If the impedances are very different most of the wave reflects (bounces off) mismatch =reflects
matching impedance
a wave tries to leave one material and enter another, if the impedance is similar/ close most of wave transmits. matching = transmits
Water narrows as it falls farther away from the faucet a) Explain b) aspirator attached to a lab faucet is turned on suction is created and water flows faster. Why?
a) Gravity. A stream of water behaves like all objects when falling, it accelerates as it falls. Since the density of water is a constant, and water tends to hold together (cohesion), the stream narrows as it is speeds up due to Bernoulli effect. Less pressure is on faster moving objects so due to narrower outlets. b_ If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.
Work and Energy Horizontal force F = 1200 N force is applied to a large box of mass m = 4 kg box sitting on a horizontal frictionless floor. In time t = 5 seconds, the box slides distance d = 30 m at constant speed along the floor. a) Find the total work done on the box by the force b) This box is not accelerated or lifted, nor is a spring compressed. Where does the energy go? c) Find the rate at which work was done (the power), in Watts.
a) Since the standard metric unit of force is the Newton and the std. metric unit of displacement is the meter, then the standard metric unit of work is a Newton•meter, defined as a Joule and abbreviated with a J. W = Fd = (1200) (30m) = 36,000 Joules b) All the energy is stored as potential energy c) Power = Work/Time = 12K(30M)/5sec. = 36K J/5 = 7200 Watts
localization
ability to determine the direction from which a sound reached us
Tensor tympani muscle
adjusts tension in eardrum, not voluntary
acceleration is constant
all objects in free fall accelerate at the same rate, and hit the ground at the same time
Tympanum
also called the tympanic membrane or the eardrum, changes sound energy energy into vibration energy. the fibrous membrane that terminates the auditory canal and is caused to vibrate by incoming sound waves
musical instruments
and forced vibration.
open end has an
antinode
Fourier's theorem
any periodic wave can be constructed by adding different amplitudes of the harmonics
overtones
any resonant frequency above the fundamental frequency
traveling waves
are observed when a wave is not confined to a give space along the medium
Scala vestibule and scala tympani
are two canals that run above and below the basilar membrane respectively; filled with liquid
Intermolecular forces are forces of _____
attraction or repulsion which act between neighboring particles (atoms, molecules or ions).
Frequency pitch of the sound depends on
area, length, and volume
the second object vibrates with increasing amplitude
as the f gets closer to the natural frequency of the nearby object
Hooke's law
as the force on a spring increases, the spring stretches proportionally. F=-kx. meaning of the spring constant, k
meatus
auditory canal; leads sound into ear, acts as a resonator, resonance frequency 3000 Hz, amplifies sounds near that frequency, tube that is closed on one end- eardrum, protects ear (wax & cilia)
Vibrating bar case 2
bar fixed at one end; tuning fork, jews harp
light does not not spreadout
because it has a very small wavelength
Low pressure storms are called cyclones (ex: hurricanes and tornados). When a hurricane is coming, the air pressure drops suddenly, causing glass windows to: __?
burst outward because air pressure outside and inside are different. In cyclones, air pressure on outside drops, so glass breaks outwards. P = f/a; F = Pascals (newtons per sq. meter) = (1.01 x 10<5> Pa) (2m x 4m) = 8.08 x 10<5> Newtons (Power = N/m<2>)
vibration in a metal bar
can be transverse or longitudinal depending on how it is created
echo
can bounce off solids and liquids, thunder, sound bouncing of clouds ( water vapor/ gas)
in gases vibrations
can only be longitudinal
Sound selectivity
can pick one sound of many, and listen to just that sound, can filter out noises you do not wish to hear
Law of Conservation of Energy
can't be created or destroyed, just change from one form to another
high frequencies
cause base to vibrate the most
Low frequencies
cause the basilar membrane to vibrate mostly at apex
Displacement
change in position, units meters (m)
Combining harmonics
forming waves with the frequency of the fundamental, but with a different wave form
semicircular canals
contribute little to nothing to hearing; they are the body's horizontal- vertical detectors necessary for balance
subjective measurement: timbre (quality)
depends mostly on overtones
subjective sound measurement: loudness
depends on intensity
Damage to ear
depends on loudness and duration
Controls motion on Earth
gravity
wavelength
distance a wave travels in a vibration; crest to crest in meters
for an object in free fall (no forces but gravity) near
earth, gravity= 32 ft/ s^2 = 9.8 m/s^2
sound reflection
echo
Law of conservation of energy
energy can be neither created nor destroyed, but can be changed from one form to another
Venturi meter measures the rate of
flow in a tube or pipe
nth harmonic: fn (string)
fn = v/λ = nv/2L = nf1
Newton's third law (action and reaction)
for every action there is an equal and opposite reaction
Mechanical work is defined when an object moves a distance X against a force f, so the force multiplied by the distance changed is work. work =
force x (change in distance) Units = N·m, 1N·m = 1 Joule
Friction
force felt an object moves (in opposite direction). Produces heat that dissipates into the atmosphere
friction
force felt as one object by or through another .
spring force
force needed to compress or extend a spring. Same amount of force to compress it, to stretch it . obeys hooke's law
gravity
force of attraction between two masses, closer objects are the stronger the force between them, decreases with distance
Pressure
force per area. P= F/A
Electrostatic forces
forces felt between charged objects - like charges (++) (- -) repel - unlike charges (+ -) attract
purpose of round window
gives fluid in cochlea room to vibrate
Materials through which sound travels best (best to worst)
hard solids, liquids, gases vacuum
Circular plates
have both circular and diameter symmetry just like membranes. The plates can vibrate in many complex modes which causes the sand to move into what is called Chladni's patterns showing the lines of symmetry
Friction always creates
heat
amplitude
height of wave; maximum displacement of a particle from equilibrium
Base
higher frequencies
Impedance
how hard it is for a wave to enter the material. steel has a greater impedance than air. air in tube has a greater impedance than open air
subjective measurement: pitch
how high or low the note is, depends mostly on frequency
subject measurement: perceived duration
how long it seems to last. when a note last for 5s it lasts for 3s
objective measurement: duration
how long sound lasts in seconds
Fundamental law of physics (2nd law)
if an unbalanced force is applied to an object it accelerates in the direction of the unbalanced force.
Causes forced vibrations, low amplitude (poor response)
if the f is far from the natural frequency of the nearby object
Helmholtz resonator
if you blow across the top, a sound is produced. the frequency (pitch) of the sound produced; the frequency (pitch) of the sound depends on area, length, and volume as well as the speed of sound in air
vibration in a metal bar will longitudinal
if you strike a metal bar on the end along the length
vibration in a mental bar will be transverse
if you strike the same bar perpendicular to the length
acoustic impedance
impedance for sound
Vibrations
in stapes causing oval window to vibrate which causes fluid in cochlea to vibrate which causes the basilar membrane to vibrate. the hairs from the organ of corti pick up vibrations sent to brain through auditory nerve
An acceleration of m/s^2 means your velocity
increases 4 m/s each sound
basilar membrane
is attached at the base (between the oval and the round window) and free to vibrate on the other end; both windows have a thin membrane over them; the stapes is attached to the oval window
Work
is done on an object when you transfer energy to that object. if one object transfers (gives) energy to the second object, the the first object does work on the second objects
Pressure example: a lynx, whose foot is three time larger than other cats its size
its foot is like a snowshoe, the large paw allows it to walk on snow by distributing the weight over a large area, and reducing pressure
moving
kinetic
Electrostatic force
like charges repel, unlike charges attract. creates force between molecules, holds molecules together
lower the frequency
longer wavelength
Apex
lower frequenices
bigger the tube
lower the pitch
Units - meters per second per second
m/s<2>
Ossicles
malleus(hammer), incus( anvil) stapes (stirrup)
Intramolecular forces, the forces which keep a
molecule together. For example the covalent bond, involving the sharing of electron pairs between atoms is much stronger than the forces present between the neighboring molecules. In water, negative oxygen electrons, are attracted to positive hydrogen. So atom sides have positive or negative sides that attract other water molecules
In physics, the kinetic energy of an object is the energy that it possesses due to its
motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.
a person sitting has a
net force of zero. force pushing you down, force of chair keeping you up
Units - The SI unit of pressure is the
newton per square meter, which is called the Pascal
closed end has a
node
standing waves have
nodes and antinodes
Objective measurment: frequency
number of vibrations
work is the application
of a force over a distance . units:
diffuse reflection
off an irregular surface. notice that although the rays obey the law of reflection, parallel rays are reflected in all directions. diffuse reflection cannot create an image
musical instruments rely
on forced vibration. not strings, plate. strings in piano hit sound board
Longitudinal waves
particles vibrate parallel to direction the wave travels
transverse wave
particles vibrate perpendicular to direction the wave travels
for mechanical waves
particles vibrate to produce and carry waves like sound
Conservation of energy examples
pendulum: when it stops, energy is dissipated into heat piano: mechanical energy to sound fire: chemical energy (in wood) to heat and light incandescent bulb: electricity into heat and light solar panel: converts light into electricity
Outer ear
pinna and meatus
stopped pipes
pipes closed at one end
rarefaction of longitudinal waves
point where particles are temporarily far apart, creating a low pressure area
compression of longitudinal waves
point where particles are temporary pressed together, creating a high pressure are
stops
potential
work/ time, units joules per second or watt
power
force
push/ pull
Objective measurement: sound intensity
rate at which energy is transmited, measure pressure changes in the air. more energy to make sound more pressure change
acceleration
rate of change in velocity, units: meters per second per second
power
rate that you do work
Vibrating Membranes
refers to leather or plastic stretched across a frame( like a drum)
garble
reverberation can garble sounds, when sounds arrive out of phase
enhances sound
reverberation; in a shower
Galileo found that accleration due to gravity is the
same for all masses
Inner ear
semicircular canals, cochlea and auditory nerve
higher the frequency
shorter wavelength
Organ of corti
sits loosely on top of the basilar membrane has rows of tiny hair cells connected to auditory nerve. vibration in stapes causing oval window to vibrate which causes fluid in cochlea to vibrate which causes the basilar membrane to vibrate. the hairs from organ of corti pick up vibrations sent to brain through auditory nerve.
the organ of corti
sits loosely on top of the basilr membrane; it contains several rows of tiny hair cells attached to nerve fibers from the auditory nerve (that connects the ear to the brain)
Ossicles: acoustic relfex
small bones protect the inner ear from very loud noises and sudden pressure changes. Loud noises triggers two sets of muscles: one tightens the eardrum and the other pulls the stirrup away from the oval window of the inner ear
example of longitudinal waves
sound waves
Skull to ear
sound you produces is carried by your skull to inner ear. 50% of the sound you produce is carried to Middle/ Inner ear through the skull
Velocity
speed in a given direction, units (m/s)
diffraction of sound
spreading out of a wave, after it passes through a slit or hits an obstruction. smaller opening; greater waves. if wavelength increases, diffraction
Modes of vibration
standing waves for masses on identical springs
round window
stapes bone moves into oval window, and round window moves out, this allows movement of fluid in cochlea.
oval window
stapes rests
interface
surface separating two phases of matter, each of which may be solid, liquid, or gaseous. ... A common interface is that between a body of water and the air, which exhibits such properties as surface tension, by which the interface acts somewhat like a stretched elastic membrane.
as the force of an object increases
the acceleration increases proportionally
The more time something vibrates per second
the higher the pitch of the note
the wider the opening
the less diffraction (spreading) of the waves
Ossicles pressure action
the lever action of the ossicles provides a factor of about 1.5 in force multiplication, whereas the remaining factor of about 20 in pressure comes from the difference in the areas of the eardrum and round window (the same force distributed over a smaller area results in greater pressure)
speed of the waves on
the medium
for two masses on three identical springs, each mode has its own frequency
the mode in which the masses move together ( symmetric mode) has the lower frequency; the mode in which they move in opposite directions ( anti- symmetric mode) has the higher frequency. There are similar transverse modes vibrating horizontally and vertically. `
band shell in a park
the performer stands on the stage, and all the sounds he produces that hit the parabolic wall behind hum are aimed forward, just like the light of the headlight
if the frequency doubles
the pitch goes up 1 octave, 8 nothes
perilymph
the pressure changes in the cochlea caused by sound entering the ear travel down the fluid filled tympanic and vestibular canals which are filled with a fluid called
diffraction through a slit is observable only when
the size of the slit is on the same order of magnitude as the wavelength of the wave
Vibrating Membranes
the skin acts like a two dimensional string ( circle modes and diameter modes), the overtones are not the harmonics
Cochlea
the spiral organ of the inner ear containing the sound- sensing mechanism. snail- shell like structure divided into three fluid filled parts. Two are canals for the transmission of pressure and the third is the sensitive organ of corti which detects pressure impulses and responds with electrical impulses which travel along the auditory nerve to the brain
Example of friction: to push a refrigerator at a constant speed requires a great deal of effort
there is a great deal of friction between the refrigerator and the floor. although you can never eliminate friction entirely, you can reduce it by putting it on wheels; and this makes it easier to moves.
helictrema
there is a hole through the basilar membrane near the the free end called the, this connects the canals above and below
Ossicles
three small bones of the middle ear that transmit vibrations from the eardrum to the cochlea
requirements to hear echo
time must be 0.1 s more; distance 110 ft. sound must return in 0.1 s or more otherwise the brain does not hear two separate sound. 55 ft to and from a wall. in a room full of people no echos because we are soft
period
time on complete vibration in seconds. 1/f
impedance transformer
to stop light from reflecting, smooths an impedance mismatch, impedance diff is less. more light gets in for a camera lens. cheerleaders megaphone, PINNA
crest of transverse wave
top of wave
Waves
transfer energy without contact
Middle ear
tympanum, tensor tympani muscle, Eustachian tube, Ossicles
speed
v. how fast the wave travels in each second.
Three masses on four springs
vibrates in three longitudinal modes, all three masses moving in the same direction (symmetric mode, has the lowest frequency). Outer two masses move in opposite directions, the center mass remains stationary (anti- symmetric mode, has the highest frequency), outer two masses move in the same direction with the same speed, the center mass moves in the opposite direction
Two masses on three identical spring
vibrates in two longitudinal modes; both masses moving in the same direction at the same speed, each mass moving in the opposite direction at the same speed.
One mass on two identical springs
vibrates longitudinally; left- and- right. There are also two transverse modes ( one on and out out of page, one up and down); mathematically these are identical
Forced (sympathetic) vibration
vibrating air hits at interface, atoms or molecules in material vibrate at the same frequency, sound transmitted. one vibrating object causes second near by object to vibrate at same frequency can occur without contact
in solids
vibrations can be longitudinal or solids
example of transverse wave
water waves
standing waves
wave confined to a given space in a medium and still produce a regular wave pattern that is readily discernible admist the motion of the medium
What problems would we face if our hearing were only slightly more sensitive to loudness than it is
we have very sensitive hearing, if it was more sensitive you would hear your bones moving and your blood flowing
Objective sound measurement:
what it actually is, using measuring device; frequency, intensity, duration
Resonance
when a vibrator is driven by a force that oscillates at a frequency at or near the natural frequency of the vibrator, a relatively large amplitude results
kinetic energy
when an object moves it has
First harmonic (fundamental f) (open pipe)
λ = 2L (Length of the pipe is one-half of a wavelength)
Fundamental Frequency (first harmonic): f1 (string)
λ = 2L (one half wave on the string)
Second overtone (third harmonic) (open pipe)
λ = 2L/3 (Length of the pipe is three-half wavelengths)
Third harmonic: f3(string)
λ = 2L/3 (Three half-waves on the string)
First harmonic (fundamental f) (stopped pipe)
λ = 4L (Length of the pipe is one-quarter of a wavelength)
First overtone (third harmonic) (stopped pipe)
λ = 4L/3 (he length of the pipe is three-quarters of a wavelength)
Second overtone (fifth harmonic) (stopped pipe)
λ = 4L/5 (The length of the pipe is five-quarters of a wavelength)