22
Mechanical Waves

Mechanical Waves

  • Upload
    oakes

  • View
    50

  • Download
    0

Embed Size (px)

DESCRIPTION

Mechanical Waves. Pendulum. Swinging mass in harmonic motion due to gravity. Time and number of swings are most useful data you will collect. Period ( T ). Time required to make one complete swing. seconds. Frequency (f). The number of swings in a certain time. - PowerPoint PPT Presentation

Citation preview

General

Mechanical Waves PendulumSwinging mass in harmonic motion due to gravity.

Time and number of swings are most useful data you will collect

Day 1 after pendulum labTime required to make one complete swing.seconds Period (T)Frequency (f)The number of swings in a certain time. swings per second = 1/s = Hertz (Hz)Day 1 after pendulum labT and f are related

or

Day 1 after pendulum labFrequencyPeriod

Day 1 after pendulum labExamples of FrequencyWhat is the frequency of the second hand of a clock?Frequency = 1cycle/60 sPeriod = 60 s What is the frequency of US Presidential elections?Frequency = 1 election/4 yrsPeriod = 4 yrs

Day 1 after pendulum labWAVE MOTIONEnergy is transferred by particle interaction or through waves.A mechanical wave is a regular repeating disturbance which allows the transmission of energy through a medium (matter). The medium does not move along with the wave.Day 2 before slinky lab

Medium does not travel

TRANSVERSE WAVESThe direction in which the energy is transferred through a wave is called the propagation of a wave The particles of the medium vibrate perpendicular to the propagation of a transverse wave

Day 2 before slinky lab

Picture of a Transverse WaveA - AmplitudeACrestTrough WavelengthlRest positionDay 2 before slinky lab

WAVE SPEEDThe average speed is defined as

Day 4

For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T). Thus

orDay 4

is true for all waves.

Note: v is dictated by the medium. f is dictated by the source. l is dependent on the n and f

Day 4

LONGITUDINAL WAVESParticles vibrate parallel to the propagation of the wave

Rest Position| | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Wave |||| | | | | | | | | | | | | | | | | |||| | | | | | | | | | |

compressionrarefactionwavelengthDay 4

Natural FrequencyAll materials have a natural frequency of vibrationThe longer an object the lower the natural frequency - pendulumThe thicker the material the lower the natural frequency guitar stringsLess tension makes it thickerMore tension makes it thinnerDay 4

A number of different waves can be in the same place at the same time, the resulting combination is described as interference. Destructive interference results in a loss of amplitudeConstructive interference results in a gain of amplitude

Wave interferenceDay 4

Interference in a Slinky

Interference in water

Car blinker interference

Pendulum interferenceThere is no vibration at a node.There is maximum vibration at an antinode.l is twice the distance between successive nodes or successive antinodes.

l

Day 4

Standing WavesWhen two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is standing still.When a wave is reflected off a fixed boundary it flips over. If the waves are produced at a multiple of the mediums natural frequency, you will not observe the propagation of the wave, only the oscillation.

Day 4

Chart1000.017452406400.034899496700.052335956200.069756473700.087155742700.104528463300.121869343400.13917310100.15643446500.173648177700.190808995400.207911690800.224951054300.241921895600.258819045100.275637355800.292371704700.309016994400.325568154500.342020143300.358367949500.374606593400.390731128500.406736643100.422618261700.438371146800.453990499700.469471562800.484809620200.500.515038074900.529919264200.54463903500.559192903500.573576436400.587785252300.601815023200.615661475300.62932039100.642787609700.65605902900.669130606400.681998360100.694658370500.707106781200.719339800300.731353701600.743144825500.754709580200.766044443100.777145961500.788010753600.7986355100.809016994400.819152044300.829037572600.838670567900.848048096200.857167300700.866025403800.874619707100.882947592900.891006524200.898794046300.90630778700.913545457600.920504853500.927183854600.933580426500.939692620800.945518575600.951056516300.95630475600.961261695900.965925826300.970295726300.974370064800.978147600700.981627183400.98480775300.987688340600.990268068700.992546151600.994521895400.996194698100.997564050300.998629534800.99939082700.99984769520100.999847695200.99939082700.998629534800.997564050300.996194698100.994521895400.992546151600.990268068700.987688340600.98480775300.981627183400.978147600700.974370064800.970295726300.965925826300.961261695900.95630475600.951056516300.945518575600.939692620800.933580426500.927183854600.920504853500.913545457600.90630778700.898794046300.891006524200.882947592900.874619707100.866025403800.857167300700.848048096200.838670567900.829037572600.819152044300.809016994400.7986355100.788010753600.777145961500.766044443100.754709580200.743144825500.731353701600.719339800300.707106781200.694658370500.681998360100.669130606400.65605902900.642787609700.62932039100.615661475300.601815023200.587785252300.573576436400.559192903500.54463903500.529919264200.515038074900.500.484809620200.469471562800.453990499700.438371146800.422618261700.406736643100.390731128500.374606593400.358367949500.342020143300.325568154500.309016994400.292371704700.275637355800.258819045100.241921895600.224951054300.207911690800.190808995400.173648177700.15643446500.13917310100.121869343400.104528463300.087155742700.069756473700.052335956200.034899496700.0174524064000-0.01745240640-0.03489949670-0.05233595620-0.06975647370-0.08715574270-0.10452846330-0.12186934340-0.1391731010-0.1564344650-0.17364817770-0.19080899540-0.20791169080-0.22495105430-0.24192189560-0.25881904510-0.27563735580-0.29237170470-0.30901699440-0.32556815450-0.34202014330-0.35836794950-0.37460659340-0.39073112850-0.40673664310-0.42261826170-0.43837114680-0.45399049970-0.46947156280-0.48480962020-0.50-0.51503807490-0.52991926420-0.5446390350-0.55919290350-0.57357643640-0.58778525230-0.60181502320-0.61566147530-0.6293203910-0.64278760970-0.6560590290-0.66913060640-0.68199836010-0.69465837050-0.70710678120-0.71933980030-0.73135370160-0.74314482550-0.75470958020-0.76604444310-0.77714596150-0.78801075360-0.798635510-0.80901699440-0.81915204430-0.82903757260-0.83867056790-0.84804809620-0.85716730070-0.86602540380-0.87461970710-0.88294759290-0.89100652420-0.89879404630-0.9063077870-0.91354545760-0.92050485350-0.92718385460-0.93358042650-0.93969262080-0.94551857560-0.95105651630-0.9563047560-0.96126169590-0.96592582630-0.97029572630-0.97437006480-0.97814760070-0.98162718340-0.9848077530-0.98768834060-0.99026806870-0.99254615160-0.99452189540-0.99619469810-0.99756405030-0.99862953480-0.9993908270-0.99984769520-10-0.99984769520-0.9993908270-0.99862953480-0.99756405030-0.99619469810-0.99452189540-0.99254615160-0.99026806870-0.98768834060-0.9848077530-0.98162718340-0.97814760070-0.97437006480-0.97029572630-0.96592582630-0.96126169590-0.9563047560-0.95105651630-0.94551857560-0.93969262080-0.93358042650-0.92718385460-0.92050485350-0.91354545760-0.9063077870-0.89879404630-0.89100652420-0.88294759290-0.87461970710-0.86602540380-0.85716730070-0.84804809620-0.83867056790-0.82903757260-0.81915204430-0.80901699440-0.798635510-0.78801075360-0.77714596150-0.76604444310-0.75470958020-0.74314482550-0.73135370160-0.71933980030-0.70710678120-0.69465837050-0.68199836010-0.66913060640-0.6560590290-0.64278760970-0.6293203910-0.61566147530-0.60181502320-0.58778525230-0.57357643640-0.55919290350-0.5446390350-0.52991926420-0.51503807490-0.50-0.48480962020-0.46947156280-0.45399049970-0.43837114680-0.42261826170-0.40673664310-0.39073112850-0.37460659340-0.35836794950-0.34202014330-0.32556815450-0.30901699440-0.29237170470-0.27563735580-0.25881904510-0.24192189560-0.22495105430-0.20791169080-0.19080899540-0.17364817770-0.1564344650-0.1391731010-0.12186934340-0.10452846330-0.08715574270-0.06975647370-0.05233595620-0.03489949670-0.01745240640-000.017452406400.034899496700.052335956200.069756473700.087155742700.104528463300.121869343400.13917310100.15643446500.173648177700.190808995400.207911690800.224951054300.241921895600.258819045100.275637355800.292371704700.309016994400.325568154500.342020143300.358367949500.374606593400.390731128500.406736643100.422618261700.438371146800.453990499700.469471562800.484809620200.500.515038074900.529919264200.54463903500.559192903500.573576436400.587785252300.601815023200.615661475300.62932039100.642787609700.65605902900.669130606400.681998360100.694658370500.707106781200.719339800300.731353701600.743144825500.754709580200.766044443100.777145961500.788010753600.7986355100.809016994400.819152044300.829037572600.838670567900.848048096200.857167300700.866025403800.874619707100.882947592900.891006524200.898794046300.90630778700.913545457600.920504853500.927183854600.933580426500.939692620800.945518575600.951056516300.95630475600.961261695900.965925826300.970295726300.974370064800.978147600700.981627183400.98480775300.987688340600.990268068700.992546151600.994521895400.996194698100.997564050300.998629534800.99939082700.99984769520100.999847695200.99939082700.998629534800.997564050300.996194698100.994521895400.992546151600.990268068700.987688340600.98480775300.981627183400.978147600700.974370064800.970295726300.965925826300.961261695900.95630475600.951056516300.945518575600.939692620800.933580426500.927183854600.920504853500.913545457600.90630778700.898794046300.891006524200.882947592900.874619707100.866025403800.857167300700.848048096200.838670567900.829037572600.819152044300.809016994400.7986355100.788010753600.777145961500.766044443100.754709580200.743144825500.731353701600.719339800300.707106781200.694658370500.681998360100.669130606400.65605902900.642787609700.62932039100.615661475300.601815023200.587785252300.573576436400.559192903500.54463903500.529919264200.515038074900.500.484809620200.469471562800.453990499700.438371146800.422618261700.406736643100.390731128500.374606593400.358367949500.342020143300.325568154500.309016994400.292371704700.275637355800.258819045100.241921895600.224951054300.207911690800.190808995400.173648177700.15643446500.13917310100.121869343400.104528463300.087155742700.069756473700.052335956200.034899496700.0174524064000

l

SINE00000050.0871557427010.01745240640100.1736481777020.03489949670150.2588190451030.05233595620200.3420201433040.06975647370250.4226182617050.08715574270300.5060.10452846330350.5735764364070.12186934340400.6427876097080.1391731010450.7071067812090.1564344650500.76604444310100.17364817770550.81915204430110.19080899540600.86602540380120.20791169080650.9063077870130.22495105430700.93969262080140.24192189560750.96592582630150.25881904510800.9848077530160.27563735580850.99619469810170.292371704709010180.30901699440950.99619469810190.325568154501000.9848077530200.342020143301050.96592582630210.358367949501100.93969262080220.374606593401150.9063077870230.390731128501200.86602540380240.406736643101250.81915204430250.422618261701300.76604444310260.438371146801350.70710678120270.453990499701400.64278760970280.469471562801450.57357643640290.484809620201500.50300.501550.42261826170310.515038074901600.34202014330320.529919264201650.25881904510330.54463903501700.17364817770340.559192903501750.08715574270350.5735764364018000360.58778525230185-0.08715574270370.60181502320190-0.17364817770380.61566147530195-0.25881904510390.6293203910200-0.34202014330400.64278760970205-0.42261826170410.6560590290210-0.50420.66913060640215-0.57357643640430.68199836010220-0.64278760970440.69465837050225-0.70710678120450.70710678120230-0.76604444310460.71933980030235-0.81915204430470.73135370160240-0.86602540380480.74314482550245-0.9063077870490.75470958020250-0.93969262080500.76604444310255-0.96592582630510.77714596150260-0.9848077530520.78801075360265-0.99619469810530.798635510270-10540.80901699440275-0.99619469810550.81915204430280-0.9848077530560.82903757260285-0.96592582630570.83867056790290-0.93969262080580.84804809620295-0.9063077870590.85716730070300-0.86602540380600.86602540380305-0.81915204430610.87461970710310-0.76604444310620.88294759290315-0.70710678120630.89100652420320-0.64278760970640.89879404630325-0.57357643640650.9063077870330-0.50660.91354545760335-0.42261826170670.92050485350340-0.34202014330680.92718385460345-0.25881904510690.93358042650350-0.17364817770700.93969262080355-0.08715574270710.94551857560360-00720.951056516303650.08715574270730.95630475603700.17364817770740.961261695903750.25881904510750.965925826303800.34202014330760.970295726303850.42261826170770.974370064803900.50780.978147600703950.57357643640790.981627183404000.64278760970800.98480775304050.70710678120810.987688340604100.76604444310820.990268068704150.81915204430830.992546151604200.86602540380840.994521895404250.9063077870850.996194698104300.93969262080860.997564050304350.96592582630870.998629534804400.9848077530880.99939082704450.99619469810890.999847695204501090104550.99619469810910.999847695204600.9848077530920.99939082704650.96592582630930.998629534804700.93969262080940.997564050304750.9063077870950.996194698104800.86602540380960.994521895404850.81915204430970.992546151604900.76604444310980.990268068704950.70710678120990.987688340605000.642787609701000.98480775305050.573576436401010.981627183405100.501020.978147600705150.422618261701030.974370064805200.342020143301040.970295726305250.258819045101050.965925826305300.173648177701060.961261695905350.087155742701070.9563047560540001080.951056516301090.945518575601100.939692620801110.933580426501120.927183854601130.920504853501140.913545457601150.90630778701160.898794046301170.891006524201180.882947592901190.874619707101200.866025403801210.857167300701220.848048096201230.838670567901240.829037572601250.819152044301260.809016994401270.7986355101280.788010753601290.777145961501300.766044443101310.754709580201320.743144825501330.731353701601340.719339800301350.707106781201360.694658370501370.681998360101380.669130606401390.65605902901400.642787609701410.62932039101420.615661475301430.601815023201440.587785252301450.573576436401460.559192903501470.54463903501480.529919264201490.515038074901500.501510.484809620201520.469471562801530.453990499701540.438371146801550.422618261701560.406736643101570.390731128501580.374606593401590.358367949501600.342020143301610.325568154501620.309016994401630.292371704701640.275637355801650.258819045101660.241921895601670.224951054301680.207911690801690.190808995401700.173648177701710.15643446501720.13917310101730.121869343401740.104528463301750.087155742701760.069756473701770.052335956201780.034899496701790.0174524064018000181-0.01745240640182-0.03489949670183-0.05233595620184-0.06975647370185-0.08715574270186-0.10452846330187-0.12186934340188-0.1391731010189-0.1564344650190-0.17364817770191-0.19080899540192-0.20791169080193-0.22495105430194-0.24192189560195-0.25881904510196-0.27563735580197-0.29237170470198-0.30901699440199-0.32556815450200-0.34202014330201-0.35836794950202-0.37460659340203-0.39073112850204-0.40673664310205-0.42261826170206-0.43837114680207-0.45399049970208-0.46947156280209-0.48480962020210-0.50211-0.51503807490212-0.52991926420213-0.5446390350214-0.55919290350215-0.57357643640216-0.58778525230217-0.60181502320218-0.61566147530219-0.6293203910220-0.64278760970221-0.6560590290222-0.66913060640223-0.68199836010224-0.69465837050225-0.70710678120226-0.71933980030227-0.73135370160228-0.74314482550229-0.75470958020230-0.76604444310231-0.77714596150232-0.78801075360233-0.798635510234-0.80901699440235-0.81915204430236-0.82903757260237-0.83867056790238-0.84804809620239-0.85716730070240-0.86602540380241-0.87461970710242-0.88294759290243-0.89100652420244-0.89879404630245-0.9063077870246-0.91354545760247-0.92050485350248-0.92718385460249-0.93358042650250-0.93969262080251-0.94551857560252-0.95105651630253-0.9563047560254-0.96126169590255-0.96592582630256-0.97029572630257-0.97437006480258-0.97814760070259-0.98162718340260-0.9848077530261-0.98768834060262-0.99026806870263-0.99254615160264-0.99452189540265-0.99619469810266-0.99756405030267-0.99862953480268-0.9993908270269-0.99984769520270-10271-0.99984769520272-0.9993908270273-0.99862953480274-0.99756405030275-0.99619469810276-0.99452189540277-0.99254615160278-0.99026806870279-0.98768834060280-0.9848077530281-0.98162718340282-0.97814760070283-0.97437006480284-0.97029572630285-0.96592582630286-0.96126169590287-0.9563047560288-0.95105651630289-0.94551857560290-0.93969262080291-0.93358042650292-0.92718385460293-0.92050485350294-0.91354545760295-0.9063077870296-0.89879404630297-0.89100652420298-0.88294759290299-0.87461970710300-0.86602540380301-0.85716730070302-0.84804809620303-0.83867056790304-0.82903757260305-0.81915204430306-0.80901699440307-0.798635510308-0.78801075360309-0.77714596150310-0.76604444310311-0.75470958020312-0.74314482550313-0.73135370160314-0.71933980030315-0.70710678120316-0.69465837050317-0.68199836010318-0.66913060640319-0.6560590290320-0.64278760970321-0.6293203910322-0.61566147530323-0.60181502320324-0.58778525230325-0.57357643640326-0.55919290350327-0.5446390350328-0.52991926420329-0.51503807490330-0.50331-0.48480962020332-0.46947156280333-0.45399049970334-0.43837114680335-0.42261826170336-0.40673664310337-0.39073112850338-0.37460659340339-0.35836794950340-0.34202014330341-0.32556815450342-0.30901699440343-0.29237170470344-0.27563735580345-0.25881904510346-0.24192189560347-0.22495105430348-0.20791169080349-0.19080899540350-0.17364817770351-0.1564344650352-0.1391731010353-0.12186934340354-0.10452846330355-0.08715574270356-0.06975647370357-0.05233595620358-0.03489949670359-0.01745240640360-003610.017452406403620.034899496703630.052335956203640.069756473703650.087155742703660.104528463303670.121869343403680.13917310103690.15643446503700.173648177703710.190808995403720.207911690803730.224951054303740.241921895603750.258819045103760.275637355803770.292371704703780.309016994403790.325568154503800.342020143303810.358367949503820.374606593403830.390731128503840.406736643103850.422618261703860.438371146803870.453990499703880.469471562803890.484809620203900.503910.515038074903920.529919264203930.54463903503940.559192903503950.573576436403960.587785252303970.601815023203980.615661475303990.62932039104000.642787609704010.65605902904020.669130606404030.681998360104040.694658370504050.707106781204060.719339800304070.731353701604080.743144825504090.754709580204100.766044443104110.777145961504120.788010753604130.7986355104140.809016994404150.819152044304160.829037572604170.838670567904180.848048096204190.857167300704200.866025403804210.874619707104220.882947592904230.891006524204240.898794046304250.90630778704260.913545457604270.920504853504280.927183854604290.933580426504300.939692620804310.945518575604320.951056516304330.95630475604340.961261695904350.965925826304360.970295726304370.974370064804380.978147600704390.981627183404400.98480775304410.987688340604420.990268068704430.992546151604440.994521895404450.996194698104460.997564050304470.998629534804480.99939082704490.99984769520450104510.999847695204520.99939082704530.998629534804540.997564050304550.996194698104560.994521895404570.992546151604580.990268068704590.987688340604600.98480775304610.981627183404620.978147600704630.974370064804640.970295726304650.965925826304660.961261695904670.95630475604680.951056516304690.945518575604700.939692620804710.933580426504720.927183854604730.920504853504740.913545457604750.90630778704760.898794046304770.891006524204780.882947592904790.874619707104800.866025403804810.857167300704820.848048096204830.838670567904840.829037572604850.819152044304860.809016994404870.7986355104880.788010753604890.777145961504900.766044443104910.754709580204920.743144825504930.731353701604940.719339800304950.707106781204960.694658370504970.681998360104980.669130606404990.65605902905000.642787609705010.62932039105020.615661475305030.601815023205040.587785252305050.573576436405060.559192903505070.54463903505080.529919264205090.515038074905100.505110.484809620205120.469471562805130.453990499705140.438371146805150.422618261705160.406736643105170.390731128505180.374606593405190.358367949505200.342020143305210.325568154505220.309016994405230.292371704705240.275637355805250.258819045105260.241921895605270.224951054305280.207911690805290.190808995405300.173648177705310.15643446505320.13917310105330.121869343405340.104528463305350.087155742705360.069756473705370.052335956205380.034899496705390.0174524064054000

&FPage &P

SINE

&FPage &P

l