waves_instruction_and_practice

Name: Period: Harmonic Motion Harmonic Motion is A pendulum To be barmonic motion there mustbe a motion that repeats itself, restoring force that tries to return an oscillating back and forth. Equilibrium object to its equilibrium position. Eventually it will fose en- Pposition When a pendulum is disturbed ergy (called dampening) {moved), gravity pulls down to and come to rest in the restore the pendulum back to the center. middle, known as its « 2 Because of momentum, it goes past the equilibrium position. —_— center to the other side and back again. Unit 10:1 A bird flying is not harmonic motion: one Jforce pulls up and a different force pulls down. Also, each force pulls from the ends not the middle. Harmonic Motion Basics Cycle: the repeated part of the motion; must include all of the steps of the motion. Period (T in sec): length of time for one cycle; how long it takes for one repetition. A slower object has a bigger (fonger) petiod . Frequency (f in Hz): number of cycles per second. Motion that repeats more often is more frequent and has a higher frequency. FromA 1o C FromCiloAdis is only half the second half acycle. of the cycle. start Oy _yp end Aq\ P A B C B C The period (T} is the 0:02.0 017brfialfoftf1e ayele oc- time from A back 102, curs in the first second, so (KR . 7-2s CY W he frequency is ¥ cycle per second. f=10.5 Hz. Period and Frequency are inversely related, Period T =L OR f = ._1__ {in secs) f T Period w A (in secs) Frequency (in heriz) As period increases, the frequency decreases. As period decreases, the frequency increases. Amplitude (A in m, cm, or degrees): maximum dis- tance or angle from the equilibrium (center) position. Wider swing = more energy = more amplitude. Amplitude = %(distance side-to-side) Ex: A pendulum has a frequency Ex: A wheel has a period of of 4 Hz. Find its period. 2 seconds. Find its frequency. = f=1T f=4Hz T T=2sec —in = T=0.05 sec f=__ £=0.5Hz Amplitade never affects period or frequency! A pendulum with more amplitude moves fast, but travels a long distance. A pendulum with less amplitude moves slow, but only travels a Amplitude = Amplitude = small distance, Either way, the More energy Less energy period is the same, Harmonic Motion Graphs Cycle—from any point on the line to that same point going the same way. This graph shows 2 complete cycles. Period—measure the time for one cycle between any two identical points on the graph (top-to- top, bottom-to-bottom, etc.). Frequency—count the number of cycles in 1 second OR find the period and use £=1/T. Amplitude—measure the total distance from side-to-side (or top-to-bottom) and divide by two OR measure the distance from the equilibrium position (halfway between the peaks) to one of the peaks. cstephennuurray.com Imagine a pen attached to the bottom of a pendulum, If a piece of paper is moved beneath the pendulum as it swings, a harmonic motion graph is drawn, Period = =1cycle = (1.7520.75) 4 @ 3 g2 1 Amplitude 84 Start / A \ / \ (side-to-side) | £ 1o~ (= U(6) | E «— ‘@ -1 A Equilibrium 8 2 \ / End of \ / ]nEdnd of Position 3 v, " cycle 2™ cycle | (halfway 4 | | | | between o o o o - - = - N peaks) R End of 1™ cycle = period (T) = 1 sec " Time {sec) 1 cycle in 1 sec = frequency (f) Legal copying of this worksheet requires written permission. Copyright © 2014, C. Stephen Murray

/ (v moU e Motaon Name: Unit 10:1 Period: Harmonic Motion: Yes or No? 1. Period A. The number of cycles per second. — Albouncing ball 2. Equilibrium B. A unit of one cycle per second. endum: ’ position C. The size or strength of a cycle. . A rul lled fir i B . Ocean waves; an;ur:Ire]:sJe;' omoneside |3 Amplitade D. Time it takes to complete one cycle. A child on a swing: . . 4. Damping E. A part of motion that repeats over and A person jumping up and 5. Frequency over with a set series of events. i 1 d s « . Jumping Jacks own 6. Cycl F. Halfway between the two sides and Bouncing spring: A spinning ball: . Lycle where the motion comes to rest. 7. Hertz G. The motion dying out over time. Period, Frequency, or Amplitude? Where is the equilibrium position for Doesn’t change period. this pendulum? More of this means more energy. If the pendulum starts at C going to Increasesd asa pelndulum swin;gs back and forth faster. the right, where does 1 cycle end? Measured in cycles per second. A E Measured in meters or centimeters. B ¢ D From letter ____ to letter___ would ____ This decreases with a smaller swing. __ Ifthe frequency increases, this decreases. __ Measured in Hertz. __ Measured in seconds. ____Ifit swings back and forth slower, this decreases. ____Asit dampens, this decreases. be the amplitude. If the pendulum starts at A, how many times does it pass point Cin 1 cycle? A moving spring T o [ Where is its equilibrium position? If the spring starts at position A, how much of a cycle does it complete from A to C? If the spring moves 10 cm from C to A (side to side), how big is it’s amplitude? An spring has a period of 4 seconds. What is its frequency? A pendulum has a frequency of 3 Hz. What is its period? A pendulum takes 10 seconds to complete 2 cycles. A) What is its period? B) What is its frequency? Positionvs. Time E 1 @ Time (sec) Position vs. Time S0 — B ] -2 30 0 2 2 33 44556677 5 5 3 5 5 5 5 5 Time (sec) 1 cycle after A is 3 172 cycle after G is i 2cyclesafterDis . 1/4 cycle before Mis . # of complete cycles shownis . Period (T) = Frequency (f) = Equilibrium position = Amplitude (A) = Mark 1 cycle of the harmonic motion. Starting at 1.5 secs, when does the 2nd cycle end: Number of cycles shownis . Period (T) = Frequency (f) = Equilibrium position = Amplitude (A) = cstephenmurray.com Legal copying of this worksheel requires writlen permission. Copyright © 2014, C. Stephen Murray

Name: . . Ch12:1 Period: Standing Waves We know that waves move. Yet waves can be T In . h trapped between boundaries. These are - a moving wave, the wave moves known as standing waves. crest TN away from what drives it. Waves . | that move away from arock in a : f f trough . || pond are driven by the force of the A fa stand N yd ‘Wave motion " Jjump rope is a good example of a standing | : B 3| rock pushing through the water. I I 1 To keep a stand- B ing wave going A moving wave. \ Standing wave (Harmonic) it needs to have — . [ a driven end: an Standing waves are TRAPPED =, N end that gives between boundaries, so we £ . crest | | | N energy to the show both the crest and the E] . | Wave ,> wave. Jump trough in the same place g . | motion L7 ropes have two at the same time. In reality, % » trough driven ends. though, it alternates: going up Es ~ and down, just like a jump rope. “ The places of no amplitude are called nodes. The Distance (m) places of greatest amplitude are called anti-nodes. In a standing wave, . A A graph of the fundamental wave each anti-node is one- graph of the el g 8gele Sfor this distance. half of a wavelength. ? Anti-node Anti-node The largest wave that can be + 1 Anti-node = (1/2)A produced in a certain distance is Node Node Node called the fundamental. 1t is one- [4——- 1 wavelength (3) —-——>l 2 Anti-nodes = A half of one wavelength long. Vdomo fpemaego e e duck o - N I L@ Harmonics are waves that are whole number multiples of the fundamental. Harmonics have nodes at \@7 Harmonics the boundaries. Harmonics sound louder, keep their energy longer, and take less energy to produce. W N@\ N rFirst 5 Harmonics of a Vibrating String I 1 N\ \ &/ Speed of a Standing W l % {\Q I Hy Hs HS‘—' Node Sl % /W N l(())' tiode To find the speed of a fixed string you would need to know the iy frequency of any harmonic and that harmonic’s wavelength. A, - Node P 1 wave- !((»] e Anti-node D 6m > fength ] <= Node f= i 21 Hz \’] s Anti-node <«——)\=13m > 4— Node i(nl €— Anti-node Remember that A=3m v=fL Y — Node A (wave‘lengtlz) f=21Hz v=213) s =2 antinodes! v= v =63 m/s \((’} ~— Anii-node ~— Node ot =7 Fundamental 2pd o st har- harmonic monic 3rd 4th 5th har- har- har- monic monic monic Jethed A ro o //,;’,‘\ - 7‘ /LJTIZ;(,Z,&Z/I uii‘ 2 / J A 7 f Lo ’M{‘S Examples of Fundamentals and their Harmonics . 72 . : . H(fy) H; H; Hy. Hs V= f /\‘ frves ks 1‘"’&:; 1Hz 2 Hz 3Hz 4Hz 5Hz - o ey 21z aHz | 6tz | 8H: | 10He | = gewvied (5 I 5Hz 108z | 15Hz | 20Hz | 250z P _L / :jfl [ nrerse L= 108z 200z | 30Hz | 40Hz | 50Hz J= T www.qisd. net/smurray Copyright © 2004, C. Stephen Murray

(\ ’) ’P 2 Name: A7), / oL \' : STUng I (g /\,) oVES Ch12:1 Period: B 1. Boundary A. The part that is moved to give energy. . ) . " Position vs. Time woPeviles: 2. Standing wave B. Where wave’s amplitude is greatest. yoien: 5 . C. Where the wave has no motion. e 3. Harmonic . D. A wave that is a multiple of another / Period: 4. Fundamental wave. = s s . = 5. Difvenend E. A wave that is trapped within boundaries. :g - I \ BESHiBHGs: 6. Nod F. The first harmonic of a standing wave, 8 ™ n Noge equal to 1/2 its wavelength. = o 7. Anti-node G. A place that limits a wave’s motion. h Amplitude: < 1 f= 8 m/s - 0 25 58 5 1 125 = 8 sec i Time (sec) By W= 8 Hz If a wave’s frequency is 25 Hz, what is its period? 4. T= 8§ m ring has a fundamental of 15 Hz, find the frequency - If a wave’s period is 0.1 sec, find its frequency. monic-3 (Hs). If a wave has a frequency of 50 Hz and a wavelength of 2 meters. 1f 20 Hz is the fundamental, find Hg: Find its speed. A wave’s velocity is 20 m/sec with a wavelength of 40 m. What is If 35 Hz is Hy, what is the fundamental uency? it’s frequency? 200 A E; 1 ' M One cycle: A to ;Cto ;Fto 10 \ / Half cycle: H to ;Jto ;Bto T \ BT D \ H \ ! N 2. 0 & *I f ¥ ‘ Two cycles: B to ;Dto ;Eto = 2 F b \ / L Total cycles: z2 10 Y / 4 G 20 K Wavelength: 0 1 2 3 4 5 Amplitude: Distance (m) The following table shows the frequencies of the L . armonics of different strings. Fill in the blank Spaces. Find its period: 1 2 3 rd 5 41z 6 Hz Mark the nodes and anti-nodes. 4Hz )§6 Hz 44 Hz A fellow studeyms you the frequencies-of four harmonics of a string. Which-one would you question and why? Frequencies: 12 Hz; 24 Hz; 29 Hz; 48 Hz 40 Hz www.aisd. net/smurray Copyright © 2004, C. Stephen Murray

Name: Period: Wave Actions Unit 10:4 Harmonic motion eventually stops. A pendulum will stop swinging; a wave will eventually weaken and stop. Friction or the restoring force causes the motion to lose its energy and to die out. This gradual reduction of amplitude we call damping. Ll L} This graph shows the damping of harmonic motion over time until it stops at its equilibrium position. Boundary Reactions Soft Boundaries Absorb Absorption—a wave’s energy dies out in a soft material (damping). Example: Yelling into a pillow. The soff pillow absorbs (dampens) the sound. 2N Hard Surface Absorption Hard Boundaries Reflect it hits a hard boundary. Example: yvelling against a wall, the sound Reflection—a wave bounces off when There are four ways a wave can react depending on the boundary it encounters: Absorption; Reflection; Refraction; Diffraction. ¢ wave ¢ Corners Diffract Diffraction Diffraction—a wave drags against a corner, causing that part of the wave to turn. This is how we can hear around corners and how light can be seen around corners. Example: talking to someone around a corner. Transparent Boundaries Refract Refraction— a wave bends when it crosses a boundary into a different medium and changes speed. Example: light bends as it passes from air into the lenses of eyeglasses. ir Glass Reflection wave reflects back (called an echo). Refraction Phase—a particular part of a cycle. + In-phase Out-of-phase means they means they f\.—f\_ ,’\' f\rj\—rfi are at the are at different : -4 same point in points in their Waves in-phase [~ Waves out-of-phase — — — their cycles. — o cycles. #* L‘**\ In-phase out-gf-phase i o — | — T —t +1 When two waves interact they interfere with each other. Constructive Interference—when the energy of two waves add together, This is like pushing on a person on a swing when they are moving away from you: you give them more energy and more amplitude. Two waves of small " \\ ,’ amplitude that are in- 1 1~ phase constructively interfere, combining into a wave of greater Vo \\ ,/ \\ ,, ™y amplitude. N\, s LN i N7 TN . Two singers on the Van 7N\ N\ same note cause a louder sound— constructive interference. \ NS cstep/1e nmurraQy.com Destructive Interference—when the energy of two waves subtract from each other, causing cancellation. Pushing ona person onl a swing as they are coming toward you (at the wrong time) causes the amplitude to be smaller. Two waves that are out-of- N X ,/ DN phase destructively interfere, N, N combining into a wave of smaller amplitude. Waves that - completely cancel each other it is known as complete de- structive interference. p.aN pd Modern headphones (and cars) use noise-canceling technology that transmits out-of-phase waves toward noise, canceling Legal copying of this worksheet requires written permission. it out. Copyright © 2014, C. Stephen Murray

Name: \/r\) C;L/\/\—e /4’ by _;LZ m/t«g Unit 10:4 Period: 1. Phase ‘When two waves increase amplitude. What is this bending called? light A 2. In-phase A single part of a cycle. 3. Out-of-phase When two waves decrease amplitude. CIREEEES 4. Constructive interference ‘When two waves are at different parts of their cycles. 5. Destructive E. When two waves are at the same part of interference their cycles. The light ray bends because the lens has a different w. s than air. 1. Absorption A. When a wave bends at a corner. B. The process of harmonic motion losing 2. Reftaction amplitude over time. 3. Diffraction C. When a wave is dampened inside a soft boundary. 4:Reflection D. A wave bouncing off of a hard boundary. 5.Damping E. A wave bending inside transparent objects. Draw what will happen to the — waves as they pass the two corners. Combining the above, draw what will happen to the wave as it goes A through a hole. —_— What do we call this? Absorption, Reflection, Refraction, or Diffraction? If a wave hits a hard wall, it bounces off by: 1f a wave hits a soft boundary, it dies by: Waves bending due to different speed mediums: A wave bends around a corner by: A wave bends as it passes thru a boundary by: Tile or marble makes for a loud room by: Eyeglasses magnify objects by: The following show pendulums in different phases of a cycle. A. C. \ D. O g 0 — s «° Which letter is in-phase with G? With How bats see at night with sound (echolocation): Which letter is 180° out-of-phase of E? ___ With H? < Carpet can keep a room quiet by: Which letter is 90° out-of phase of F? with G? Light comes back from a mirror by: Wave 1 < Wave 2 : & oF GE = 20 N/m k = 20 N/m £2 E g0 T £ oA H M M M M L i3 / \ 23 2.3 o a " -4 -4 L20~c _T LZB cm _T -5 -5 b s g 23 g || g2k g~ The above is the same\&p@g, but at different times. Position (m) ™ position (m) Amplitude of the left spring= . Right spring = What is the amplitude of wave 1? Wave 27 o Which picture is the before picture? N Why? \ Are they in-phase? What will happen if the waves combine? What will be the amplitude of the combined wave? cstephenmurray.com Legal copying of this worksheet requires written permission. Copyright © 2014, C. Stephen Murray

Name: Period: gj | What is Sound? ’ ~ Sound is the movement of compression waves (longitudinal waves) hitting our ears. These compression waves are alternating high and low pressure areas. The air molecules vibrate back and forth, but don’t travel. _, 4 Spealkers imitate | ) sounds by pushing = air and causing vibrations. Sound Unit 10:5 Sound Wave are Pressure Waves Sound source /Iow py‘g_gmlre\ human ear ® 200 © .... ) V\ high /v pressure x ~&; On graphs, Vd N | we use /_* { N crests and troughs to + % 7‘ show high and low B k| pressure. low pressure Tiny hairs inside the translate air pressure As a wave sound needs a medium to travel through. Sound cannot travel through the vac- uum of space. Space is silent (no matter what you hear in the movies). cochlea (inner ear) into electrical im- pulses that can be read by the brain. Very loud sounds bend these hairs, causing deafness. ‘x' Frequency = Pitch We hear the frequency of sound as pitch. A higher frequency we hear as a higher pitch. A lower frequency we hear as a lower pitch. Fa AL//O tunoleretond stadt gfl / n owo exprio- Higher Frequency = Higher Pitch Frequency (f) Wavelength () Source Elephants and submarines use infrasonic sound (too low to hear) to communicate over long distances. Very low frequencies (very bass) travel very long distances and can penetrate 20 Hz 17m rumble of thunder 100 Hz 34m bass guitar 2,000 Hz 17 em fire truck siren 4,000 Hz 7 cm highest note of piano 10,000 Hz 3.4 cm whine of a jet turbine through water (just like thru cars). Humans can hear frequencies that are between 20 Hz and 20,000 Hz! Dog whistles use ultra- sonic frequencies (above human hearing [+20,000 Hz]), but perfect for dog ears! —jj‘l Amplitude = Loudness I Loudness is measured in decibels (dB) A +10 dB change we We hear pressure (the amplitude) of sound as ”pffi@ Ke loudness. Tt takes more energy to create a louder sound. Too loud of a sound can cause deafness. 10 dB Total silence. hear as twice as loud. 30 dB Total quiet in the woods at night. A 30 dB sound is twice as - loud as a 20 dB sound. 60 dB Normal conversation. 70 dB Busy traffic in the city. A -10 dB change we 90 dB A jackhammer (hearing damage if not protected) hear as half as loud. 110 dB Threshold of pain from sound. A 30 dB sound is half as 200 dB Human will die from the sound pressure. loud as 2 40 dB sound. Speed of Sound (v) The speed of sound changes. In gases, hotter (faster) gases conduct sound faster. In solids The speed of sound in air is about 340 m/sec. You can use v, = fi. to find frequency or wavelength. AND use S =D/T to find distance or time. In both cases, Vs (8) is a constant for sound: 340 /m p&%&mf OnleclpFrox3 and liquids, generally denser e (tighter) materials arc faster. \K Ex. Find the wavelength of a 200 Hz sound. "‘kj v,= 340 m/s v=f\ so A=v/f WY ESVE V, (m/sec) X £=200Hz L= (340 m/s) + (200 Hz) Air 340 8 =2 LELTm) Helium 965 1 }l:' o — T oy - N . If you hear a sound 3 seconds after you Water 1530 Q see the motion. How far away is it? Wood 2000 Q. Gold 3240 = | Vs =340 mv/s v;=D/Tso D=v,T ° ~J | T=3sec D = (340 m/! (3 sec) Steel 5940 il = cstephenmurray.com m/sec. Maotion faster than sound is called supersonic. Supersonic planes give their speed in multiples of Mach (1 x the speed of sound). Mach | =340 m/s. Mach 2 =680 ms. A sonic boom is caused by an object breaking through the sound barrier. Supersonic planes, bullets, and bullwhips all make sonic booms. Copyright © 2014, C. Stephen Murray |

S Name: =g C\z) 4 (C/ Unit 10:5 Period: 1. Sound A. Faster than the speed of sound. 1. Pitch A. Where there is no sound because of its B. A wave caused by alternating high and 2. Sonic boom low pressure 3. Supersonic C. The organ that detects sound waves. 4. Ultrasonic D. A pressure wave caused by an object go- ing faster than sound. 5. Cochlea E. A sound higher than humans can hear. vacuum. 2. dB B. How we hear changes of frequency of sound. 3. Space C. 340 m/s in air. 4. Loudness D. How we measure loudness. 5. v E. The amplitude or strength of a sound. Displacement vs. Position \ 7 1\ 41\ \ N \ TUTTO03 03~ rg— Shhbvioanpwro L N [ 5 5 b b Position (m) 1 cycle is from 1 m to Amplitude (A) = Use the graph to answer these questions: A= 3 1/2 cycle is from 0 m to Total cycles: H It is a sound wave; find frequency: Is this frequency audible to humans (can we hear it)? A wave’s velocity is 90 m/sec with a frequency of 6 Hz. What is it’s wavelength? A sound wave has a wavelength of 20 m. Find its frequency. If a sound wave’s frequency is 100 Hz. What is its period? What is the above wave’s wavelength? A railroad crew is repairing a rail. You hear the hammer 0.5 sec- onds after it is swung. How far away is the crew? You hear a plane 4 seconds after you see it. Find the distance to the plane. ‘Why is space silent? If T increase the energy I give a sound wave what changes: If a wave’s~fourth harmonic has a frequency of 40 Hz, what is its natural frequen d what is the frequency of Hg? If a wave’s fundamental is 6 Hz, what harm 48 Hz? i¢ has a frequency of Tfagsound is 40 dB loud. Answer how many dB these would be: ind i iod: Find its perio 50T Mark the nodes and anti-nodes. How many wave - is it? ‘What is its wavelength? Speed of the wave on this string: cstephenmurray.com Copyright © 2014, C. Stephen Murray