angular frequnecy

W=2∏F

alwasy start with W when graphing the shape of an oscillation

x(t)= Acos(Wt+Φ) (equation when wave is in SHM)

t = time

Φ = angle phase

An angle between 0 and 360 degrees that specifies a point in one cycle.

0 = beginning of cycle

90 = 1/4 from beginning

180 = 1/2

270 = 3/4

360 = same as 0 degrees

graphical equation = Sin(Wt)

180 degrees = half the period

cancels out sound waves

if two graphs are out of phase, they are the same shape and and everything, but flipped upside down.

2 quantities have the same period and frequncy and are not offset at all.

In phase means in sync waves.

Process by which waves appear to bend around corners

Ie. someone facing the opposite direction and the abilit to still hear them is because of diffraction.

transverse wave: the object of the wave is moving in a perindicular manner relative to the direction the wave is traveling.

the object is moving up and down along an x axis.

if polarized; the object moves in a particular direction in the plane.

the motion is ordered.

if unpolarized; moves in all directions and is the motion is random.

constant vaue of  force that is pulling or pushing the object in motion.

F = -K(x)

F = force

W =(√K/m)

Velocity

velocity as a function of time:

V(t) = -W²ASin(Wt + Φ)

x(t)

position as a function of time:

x(t) = Acos(Wt + Φ)

(a) acceleration as a function of time:

a(t) = -W²Acos(Wt +Φ)

the material that carries the energy moves in a direction that is perpindicualr to to the energy itself.

particle speed = rate at which the energy goes up and down

Deep water waves, and light waves

the material that carries the energy is moving in a paralell direction compared to the direction of the energy itself.

sound waves.

molecules move from mouth to ear in a longitudinal manner.

speed of anything = distance/time

v = x/t

f= λ/T

speed of a wave  

V= λf

v(sound) = (331+.6T_c )

unit = meters/second

if the air is hotter the wave moves faster, and vice versa if the air is colder.

(25 m/s = 60 mph)

345 m/s

use this assumption when speed and temperature are not given

345 m/s 

20 Hz

= 17.5 meters = maximum wavelength

345 m/s

20,000 Hz

= 17.25 mm = 1.725 cm = minimum

(10 mm = 1 cm)

all parts of a wave act as sources of spherical waves in three dimensions

ie: old waves make new waves like the ripple effect on water.

if a wave spreads out in all directions (three dimensions) then its intensity will decrease in proportion to the square of the distance from its source.

ie: three dimension 5x the distance = intensity will decrease 25 times.

two dimensions the intensity will decrease in proportion to the distance

ie: 5x the distance = intensity will decrease by 5

reflection occurs when a wave bounces off of a boundry between two differnt materials.

Th angle of the incident = the angle of reflection

25 degree angle of incident = 25 degree angle of reflection

occurs when the wave changes direction due to crossing through a boundry betwen two different materials.

wave bends

light traveling through glass changes direction

when a wave begins to disperse through space and spread as it moves further and further.

the lower the frequency the higher the dispersion, and vice versa for higher frequency

waves don't necessarily interfere, they combine in two different manners having different effects

when two or more waves with the same frequency fromm different sources combine at some point

when waves interfere spatially the resulting two extreemes are constructive and destructive

percents out of 100%

constructive = in phase

ie: 37% constructive/63% destructive

used for audio mixng

destructive spatial interference = out of phase

used for kareoke

refers to the pressure change

constructive:  two waves with same graphical patterns cmbine

results in increase in pressure change

destructive: two waves with opposite graphical pattersn combine and cancel eachother out.

pressure change is (wave one - wave two)

when waves interfere in time

two waves, different frequencies, same source, combine some point in space, two things could happen:

1. the frequency heard will be the average of the  two frequencies:

f(average frequency of combined wave) =

f₁ + f₂

2

2. the combined wave will get louder and softer at a rate equal to the absolute value of the of the difference between the two frequencies.

f(beat) = absolute (f₁-f₂)

(in tune frequency = 0)

if the source of the sound wave and/or the listener are moving with respect to the material carrying the sound wave, then the frequency heard by the listener will be different  than the frequency emitted by the source

most commonly used to calculate speed of listener, or source.

effects the wavelength as well

f₀ = V +/- V_o

V +/- V_s

do not compare the source ot the observer, compare it to the material carrying the wave.

if the source and listener are moving toward eachother the frequency heard will be higher than the frequency emitted by the source.

doppler effect:

equations for different possibilities

4 possibilities relative to material

1. S approaching, O approaching

= + numerator/- denominator

2. S approaching, O receeding

= - numerator/ - denominator

3. S receeding, O receeding

= - numerator/+ denoinator

4. S receeding, O approaching

= + numerator/+denominator

Doppler effect:

material carrying wave is moving

ie: air = wind speed

ie: source approaching moving 20 m/s

observer receeding moving 10 m/s

material moving 5 m/s toward 

= source actually moving at 15 m/s

observer actually moving 5 m/s

material actually moving 0 m/s

shock waves occur when object is moving faster than the speed of sound

not periodic

sound waves that have a frequncy greater than 20,000 Hz

Sonar, medical imaging, material analysis, ultrasonic cleaning, dow whistles, echolocation, cavitation research

sound waves with frequency less than 20 Hz

cruisers with loud subwoofers, earthquakes, thunder, underground imaging (palentology, archeology, geology, natural resources), motion sickness.

one wave that travels in only one direction

result of two identical waves traveling in opposite directions that undergo constructive spatial interference

often results from one wave that undergoes reflection at one or two places.

f = fundamental frequency

L = langth of string

F = force of tension apllied to the string

W = mass per unit length of string (density x area)

f = (1/2L)√(F/W)

Mersennes law:

length, tension, mass per unit length

1. length; longer strings produce lower notes; violin, viola, cello, bass

2. tension: greater tension creates higher notes; tuning a guitar or piano

(if increased from 5lbs to 10lbs, tension dos not double, watch for √)

3.  mass per unit langth; thicker create lower notes; strings on a piano

(if you make a string 2x as thick, the area increase 4x, which = 1/2 the frequency)

equal to teh speed of the wave divided by twice the length of the string

(only applies to string/wire)

speed of a wave = √(F/W)

string instruments:

modes of excitation

bowing; violin, viola, cello, etc. uses friiction, string stretches creating triangular displacment.  Linear restoring force.  

plucking; guitar, harp, harpschord, etc. spherical displacement

striking; piano, hammer dulcimer, etc.

the air at the closed end cannot vibrate, and the air at the open end can.

creates a longitudal wave, molecules move towards open end of tube.

air at the open end always antinode (maximum amplitude)

clarinet, and bass clarinet

general equation = λ = (4L)/N

N = harmonic number, and is always odd

the air at bothe ends can vibrate.

string instruments work the same way

air molecules are moving like an accordian from the center of the tube; they move outward then inward after half a period.

base on node placement

f_N = (Nv)/(2L)

ie; 1 node λ = 2L

2 nodes λ  = L

3 nodes λ  = (2/3)L

1 standing wave = 1 node/1 harmonic

2 = 3 node/3 harmonic

3 = 5 node/5 harmonic

1st node/harmonic = fundamental frequency

3rd node/harmonic= 1st overtone

5th = 2nd overtone

7th = 3rd overtone

piccolos, flutes, and bass flutes

recorders

soprnao, alto, tenor, bass sax

oboes, and bassoons

all brass instruments

acts like cylindrical open

organ pipes, flutes

mode of excitation

single or double

mode of excitation

single; clarinets and saxaphone

double oboes and bassons

change the effective length

side holes; flute, clarinet, saxophone

valves; trumpet, tuba, french horn

slide; trombone, penny whistle

register keys; supresses fundamental to produce the next possible harmonic

over blowing; adds more energy to the air allowing for higher harmonics

related to the tone, note or pitch that is heard

larger freq. = higher notes, and vice versa for low freq.

related to the loudness that is heard

large amp = louder