Waves Unit / Mechanical Waves Sub-Unit

Waves Unit / Mechanical Waves Sub-Unit 5.1.1 Oscillatins - time fr ne scillatin - number f scillatins per secnd Equatin Pendulum Mass n a Spring PRACTICE Regents Physics 1. A pendulum is timed as it mves frm its starting pint A t several ther psitins as it swings. A B C D a. Use the data frm the psitin/time chart t determine the perid f the pendulum. s b. Calculate the frequency f the pendulum. E L Psitin A B C D E Elapsed Time 0.00 s 0.20 s 0.40 s 0.60 s 0.80 s start start c. Use the perid f the pendulum t calculate the length f the pendulum string. Equatin Equatin 2. A spring and mass system has a perid f 0.45 secnds. The spring cnstant f the spring is 300 newtns per meter. Determine the amunt f mass n the spring. 1 P a g e

Review Questins 5.1.1 Explain the relatinship between the perid f a pendulum and the factrs invlved in building ne. Explain the relatinship between the perid f a mass scillating n a spring and the factrs invlved in building ne. - Hw lng des it take fr a pendulum with a frequency f 2.0 hertz t cmplete ne full scillatin? - Fur pendulums are built as shwn in the table belw: Pendulum Mass Length A M L B 2M L C M 2L D 2M 2L - Determine the perid f a pendulum with a length f 40 centimeters. [0.5s] [1.3s] Which statements belw are true? (a) Pendulums A and B have the same perid. (b) Pendulums A and C have the same perid. (c) Pendulums C and D have the same perid. (d) Pendulums B and D have the same perid. (e) Pendulum A has a shrter perid than pendulum B. (f) Pendulum A has a shrter perid than pendulum C. - An astrnaut ntes that n planet P it takes 1.5 secnds fr a pendulum with a length f 0.50 meter t cmplete ne full scillatin. What is the acceleratin due t gravity n planet P? - Fur masses are hung n fur springs as shwn in the table belw: [a, c, f] [8.8m/s 2 ] - A 2.0 kilgram mass is hung n a spring with a spring cnstant f 100 newtns per meter. What perid will the mass scillate back and frth with? What frequency will this scillatin have? [0.9s] System Mass Spring Cnstant A M k B M 2k C 2M k D 2M 2k Which statements belw are true? (a) Systems A and B have the same perid. (b) Systems A and C have the same perid. (c) Systems A and D have the same perid. (d) System A has the shrtest perid. (e) System B has the shrtest perid. (f) System C has the shrtest perid. [1.1Hz] [c, e]

Waves Unit / Mechanical Waves Sub-Unit Regents Physics 5.1.2 Pulses Definitins - a single vibratry disturbance Transmits ENERGY but nt MASS befre Fast Slw befre Slw Fast - height abve equilibrium and directly related t ENERGY. - a cntinuum f particles f the same type that stres and releases energy. after after As a pulse travels in a medium it Phenmenn #1 - Reflectin befre Fixed Pint befre Flating Pint Cnstructive Phenmenn #2 - Interference Destructive after after If a pulse changes mediums it 3 P a g e

PRACTICE 1. Sketch a pulse that shws the superpsitin f the pulse pairs belw. Amp = +1 Amp = +1 Review Questins 5.1.2 Explain the definitin f a pulse. Explain reflectin and superpsitin f pulses. - Which f the fllwing is transmitted by a pulse? (1) energy and mass (2) mass nly (3) energy nly Amp = +3 Amp = -0.5 - The energy cntained in a pulse is related t its: (1) amplitude and speed (3) width and speed (2) amplitude nly (4) speed nly - As pulses travel they lse: (1) amplitude and speed (3) width and speed (2) amplitude nly (4) speed nly Amp = +2 Amp = -2 [3; 2; 2] Amp = -1 Amp = +1 2. A pulse with a height f +0.5 meter encunters a secnd pulse with a height f +2.3 meters. a. The tw pulses interfere: b. The resulting height f the medium when the pulses interfere will be: m - A pulse mves frm a very thick rpe int a thin string. Circle the term that makes the statement true. (a) The transmitted pulse will lse / gain amplitude. (b) The transmitted pulse will lse / gain speed. (c) The transmitted pulse will lse / gain energy. (d) The reflected pulse will / will nt cme back n the ppsite side. Sketch the superpsitin f the fllwing sets f pulses. [gain; gain; lse; will nt] 3. A pulse with an amplitude f 0.4 meter mves frm a thick, heavy crd where its speed is 2.0 meters per secnd int a much thinner string. The speed and height f the pulse after it is transmitted culd be: (1) Amplitude = 0.5 m; Speed = 1.0 m/s (2) Amplitude = 0.3 m; Speed = 1.0 m/s (3) Amplitude = 0.5 m; Speed = 3.0 m/s (4) Amplitude = 0.3 m; Speed = 3.0 m/s

Waves Unit / Mechanical Waves Sub-Unit 5.1.3 Wave Prperties Definitins and Types f Waves - a regularly repeating pulse. Transverse Wave particles f the medium mve t the wave s directin f travel. v λ Wave Velcity Waves have a definite directin f travel. Regents Physics Wave perid (T) = Wave frequency (f) = IMPORTANT: ONCE A WAVE IS PRODCUED ITS FREQUENCY CANNOT BE CHANGED! Wavelength (λ)= Equatin A Because frequency is always the same, if a wave changes speed (mediums), its wavelength must als change. Mtin f particles in the medium Lngitudinal Wave particles f the medium mve t the wave s directin f travel. Example - A wave with a frequency f 1.5 hertz is mving thrugh a heavy spring where its wavelength is 2.0 meters. What is the speed f this wave? v λ What wavelength wuld the wave have if it mved int a lighter spring where its speed was 6.0 meters per secnd? Mtin f particles in the medium What wuld prbably happen t the amplitude f this wave after it mves int the lighter spring? 5 P a g e

Wave Phase What is the directin f mtin in the medium? PRACTICE 1. What is the speed f a water wave with a wavelength f 10 meters if it has a frequency f 0.15 Hz? v v Tw pints are cnsidered t be in phase if they are mving in the same directin at the same time. 2. A man n a beach ntices that fur waves arrive n the shre every 20 secnds. What is the frequency f the waves? The number f degrees ut f phase depends n the difference in wavelength between the pints. 0 = 90 = 180 = A D v 3. A sund wave travels frm air t metal. What happens t its speed as it makes this change? B E F F C 4. Why is the sund frm a speaker luder when yu sit clser t it?

Waves Unit / Mechanical Waves Sub-Unit Review Questins 5.1.3 Use equatins t determine wave speed, wavelength, perid, r frequency. Understand the difference between lngitudinal and transverse waves. Explain hw amplitude and wavelength are measured. Explain the cncept f phase. Explain the directin f particle mtin in a medium. - What is speed f a wave with a frequency f 10 hertz if its wavelength is 3 meters? Regents Physics - Mark each diagram r statement with a T if it describes a transverse wave r an L if it describes a lngitudinal wave. [30m/s] Particles in this type f wave mve parallel t the directin f wave travel. Particles in this type f wave mve perpendicular t the directin f wave travel. - What is the wavelength f a wave with a frequency f 6 hertz if it is mving at 30 meters per secnd? This wave mves mre quickly in dense mediums than sparse nes. This wave mves mre quickly in sparse mediums than dense nes. [5m] - What is the frequency f a wave that is mving at 15 meters per secnd if its wavelength is 7.5 meters? What is this wave s perid? - What is the wavelength f each f the waves shwn belw? a. b. [2Hz; 0.5s] 2 m 6 m c. d. 12 m 0.4 m e. 4.5 m [2m; 6m; 4m; 0.8m; 3m] 7 P a g e

- What is the amplitude f each f the waves shwn belw? 5.1.4 Interference, Standing Waves, and Resnance Intrductin and Terms 0.5 m 2.0 m - the result f tw waves meeting in a medium. - results in greater amplitude. [0.25m; 2m] - Pick a set f pints that are: (a) in phase (b) 90 ut f phase (c) 180 ut f phase - results in lwer amplitude. In phase interferes A B C D [BD; AB,BC; AC,BD] 180 ut f phase interferes - Determine the directin in which each particle shwn in the diagram will mve in the next instant f time if the wave mves t the right. A B v C D [ ] - In which type f wave will particles mve nrth and suth if the wave travels east t west? (1) lngitudinal (3) circular (2) transverse (4) trsinal E [2] Between 0 and 180 results in different amunts f interference at different pints. - Hw will particle A mve in the wave shwn belw? A (1) (3) (2) (4) [3]

Waves Unit / Mechanical Waves Sub-Unit Regents Physics crest (wave frnt) trugh Interference f Tw Pint Surces f Waves Phenmenn #4 - Resnance All mediums have a that crrespnds t their atmic structure. Exciting this frequency causes large vibratins in the medium If the frequency is excited with enugh the medium may becme damaged r even shatter. If tw materials have the same (r clse) natural frequencies then vibratins may be passed frm ne material int the ther. PRACTICE 1. The grid belw represents a 10.0 meter lng string. Phenmenn #3 - Standing Waves When a wave encunters a fixed bundary it. The reflected wave cmes back thrugh the riginal wave and they. The result is a standing wave Standing wave features: : always 180 ut f phase (destructive interference) - NO MOTION. a. Sketch the standing wave that this string wuld prduce if it were t have SIX ndes. b. Draw a circle arund each ANTINODE n the string. c. Determine the wavelength f this standing wave. m d. Assuming that this wave mves at 2.0 meters per secnd, calculate its frequency and perid. : alternate between inphase and 180 ut f phase MAX MOTION. 9 P a g e

Review Questins 5.1.4 Explain the phenmenn f wave interference. Explain the rigin f and describe features f standing waves. Explain the phenmenn f resnance. - Tw pint surces prduce a pattern f verlapping circular waves. The slid lines in the diagram represent wave crests while the dtted lines represent wave trughs. Mark a C in the bxes that inidcate cnstructive interference and a D in the bxes that indicate destructive interference. A standing wave is prduced as a result f a cmbinatin f and. The main features f standing waves are: at which minimum mtin f the medium ccurs. at which maximum mtin f the medium ccurs. Determine the wavelength f the standing wave shwn belw. Identify ne nde and ne anti-nde. 5.0 m - Sketch a wave that will cmpletely destructively interfere with the wave shwn belw. What is the phase difference between these tw waves? - A (NODE/ANTINODE) is the result f an alternating phase difference f 0 and 180 degrees between tw waves passing thrugh each ther. (Circle ne) - At the pint when the tw waves shwn belw cmpletely verlap, what will the superpsitin f the tw waves lk like? Draw a sketch f the wave prduced during this interactin. v v - T prduce a standing wave, tw waves must: be mving in have the same: [reflectin, interference; nde, anti-nde] [2.5m] [anti-nde] [same directin; amplitude, frequency, wavelength]

Waves Unit / Mechanical Waves Sub-Unit Regents Physics 5.1.5 Sund and Dppler Effect Sund Facts Sund is transmitted as a wave. Mechanical wave s it requires. Speed f sund in air: m/s sea water: m/s steel: m/s Amplitude f a sund wave is synnymus with Phenmenn #5 Dppler Effect A surce sends ut waves in all directins with the same frequency and wavelength. Hw the wave is perceived by an bserver depends n f the surce and/r bserver. Same frame f reference Getting clser tgether - at increasing speed - at decreasing speed - PRACTICE 1. What is the frequency f a sund wave with a wavelength f 0.04 meter in air? What type f wave is this, transverse r lngitudinal? 2. A bat is using sund waves t lcate an insect. The bat prduces sunds with a frequency f 120 kil-hertz and ntes that the sund it transmits ech s back in 0.02 secnd. a. What is the bat s distance t its prey? Getting farther apart - at increasing speed - at decreasing speed - b. What is the wavelength f the bat s radar? 11 P a g e

3. A radar statin is tracking a dense sectin f clud cver. If the radar statin transmits energy at a frequency f 300 megahertz and receives reflected energy frm the cluds at a frequency f 150 megahertz, what can the frecasters say abut the mtin f the cluds? - Circle the terms that prperly cmplete the sentences belw. Sund is transmitted as a TRANSVERSE / LONGITUDINAL wave. Sund is prduced as a(n) MECHANICAL / ELECTROMAGNETIC wave. Sund travels mre QUICKLY / SLOWLY in water than it des in air. Explain why this is true! Review Questins 5.1.5 Explain the rigin f sund waves, the cnditins necessary fr them t exist and details regarding their transmissin. Explain the mtin f bjects in Dppler Effect diagrams. Explain frequency changes due t the Dppler Effect. - The diagram belw shws a surce f sund waves mving with a cnstant speed near an bserver. The surce prduces sund waves with a frequency f 100 hertz. Is the surce getting clser t the bserver r farther away? Observer - If a ship sends a snar signal thrugh the water t the sea flr and it bunces back t arrive back at the ship in 2.0 secnds, hw deep is the water under the ship if sund travels thrugh water at 1500 meters per secnd? Which frequencies culd the bserver be hearing as the surce appraches? (a) 80 Hz (b) 100 Hz (c) 110 Hz (d) 120 Hz - If it takes a sund wave 2.5 secnds t travel frm the spt where a lightning strike ccurs t an bserver, hw far away frm the bserver did the strike ccur? [1500m] As the surce appraches, will the frequency heard by the bserver be cnstant, increasing, r decreasing? [828m] - Why wuld an astrnaut nt be able t cmmunicate with anther astrnaut by talking in the vacuum f space? [lngitudinal; mechanical; quickly density] [clser; (d); cnstant] [n medium t cnduct the sund]

Waves Unit / Mechanical Waves Sub-Unit - A train is mving at a cnstant 35 meters per secnd away frm an bserver. As the train is mving it blasts its hrn which prduces a sund with a frequency f 1000 hertz. The bserver will perceive that the hrn s frequency is (1) less than 1000 hertz and cnstant (2) less than 1000 hertz and decreasing (3) greater than 1000 hertz and cnstant (4) greater than 1000 hertz and increasing Phenmenn #6 - Diffractin Regents Physics When a barrier blcks part f a wave-frnt nly part f the wave will pass. Because a wave-frnt is a cllectin f wavelets, the wavelet n the crner f the barrier will be able t express its curvature. This causes the way-rays t - A plice car is accelerating tward an bserver. The plice car s siren prduces a sund with a frequency f 1200 hertz. The bserver will perceive that the siren s frequency is (1) less than 1200 hertz and cnstant (2) less than 1200 hertz and decreasing (3) greater than 1200 hertz and cnstant (4) greater than 1200 hertz and increasing 5.1.6 Diffractin, Reflectin, and Refractin Huygen s Principle - a small surce f circular waves. Lined up next t ne anther they will prduce a.. - represents a wave crest. The directin in which these travel is shwn by a. [1; 4] Single-Opening Diffractin When a wave frnt passes thrugh an pening in a barrier the wave rays bend arund BOTH crners. The amunt f bending depends n the relatinship between Wavelength << Opening Size and Wavelength Opening Size - shws the directin f a wave s travel. 13 P a g e

Duble-Slit Diffractin When a wave-frnt passes thrugh tw slits at the same time it bends thrugh bth slits and the wave-frnts interfere. When a wave-ray passes frm ne medium int anther it will bend due t the difference in Phenmenn #7 - Refractin between the tw mediums. Slw medium Fast medium Bends λ Fast medium Slw medium Bends λ Regular (Specular) Reflectin Revisited Diffuse Phenmenn #8 Plarizatin A plarizer nly allws waves with particles vibrating in a specific directin t pass. This nly wrks fr waves.

Waves Unit / Mechanical Waves Sub-Unit PRACTICE 1. A wave with a wavelength f 3.0 meters passes thrugh an pening that is 0.02 meters wide. Which statement best describes what will happen t the wave? (1) The wave frnts will nt bend. (2) The wave frnts will bend t a large degree. (3) The wave frnts will bend, but nly slightly. (4) The wave will be cmpletely stpped and will nt pass. 2. Which cmbinatin will prduce the least degree f diffractin? (1) a wavelength f 2.0 m thrugh an pening f 1.0 cm (2) a wavelength f 30 m thrugh an pening f 2.0 m (3) a wavelength f 2.0 m thrugh an pening f 25 m (4) a wavelength f 5.0 nm thrugh an pening f 45 m Review Questins 5.1.6 Describe the phenmenn f reflectin; identify and sketch wave frnt diagrams in which reflectin ccurs. Explain why waves refract; identify and sketch wave frnt diagrams in which refractin ccurs. Explain the diffractin f waves. Identify and sketch wave frnt diagrams in which diffractin ccurs. Regents Physics - When waves encunter a change in medium r a barrier, sme f the energy is always and sme is always. - The diagram belw shws a series f wave frnts appraching a barrier. Sketch a set f reflected wave frnts n the diagram. 3. Which wave phenmenn relates t a. apparent bending f a pencil in a cup f water. b. buncing f light ff f a mirrr. c. bending f water waves as they pass a dck. d. selective filtering f light passing thrugh sunglasses. e. apparent change in frequency due t a mving surce. f. prductin f ndes and anti-ndes. [reflected, transmitted] - Waves refract when they change. - In which area f the diagram belw is the wave traveling mre quickly? Area 1 g. vibratins prduced at a medium s natural frequency. h. meeting f tw waves in a medium. Area 2 [speed/directin; area 1] 15 P a g e

- Waves are diffracted as they pass thrugh penings r arund barriers. Sketch the diffractin pattern in each f the three cases shwn belw. In which case is the diffractin mst prnunced? [right diagram is mst prnunced]