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

# armonic Metore Narne: Unit 10:1 Period: Which of these is Harmonic Motion? 1. Period D | &7 The number of cycles per second. " ilibri . Auni 1 S v A bouncing ball )U 2. qu{ll_xbrlum /B/ unit of one cycle per second. %) position | G The size or strength of a cycle. . A ruler pulled from one side : v s Oceanwaves: _/ ol releI;se & 3. Amplitude” | B Time it takes to complete one cycle. A child on a swing: \f . . 4. Damping Gz E’ A part of motion that repeats over and ) M A person Jufj@lng up and 5. Frequency A over with a set series of events. Toongting Jaeks: Jow: ‘ . /FG-IaIfway between the two sides and Bouncing spring: i A spinning ball: f ) . Cycle fi where the motion comes to rest. 7. Hertz [; G. The motion dying out over time. - Period, Frequency, or Amplitude? Doesn’t change period. More of this means more energy. - Increases as a pendulum swings back and forth faster. _L Measured in cycles per second. _fi Measured in meters or centimeters. _A_ This decreases with a smaller swing. _ 1~ Ifthe frequency increases, this decreases. __{ Measured in Hertz. _T_ Measured in seconds. jlfit swings back and forth slower, this decreases. Where is the equilibrium position for this pendulum? V- If the pendulum starts at C going to the right, where do% cycle end? C sind VT fl Fro letter _A to letter < would AEA g B s If the pendulum starts at ‘A, how many times does it pass point Cin1 cycle? 'T von S An spring has a period of 4 seconds. What is its frequency? A As it dampens, this decreases. = Ysgeo S T e T=4 ==y =25 b=z A moving spring Where is its equilibrium position? £= | =2 A pendulum has a frequency of 3 Hz. What is its period? A -L/\/\/\/v\?\, M | Ifthe spring starts at position A, how = : much of a cycle does it complete 1;-&2" it T= ’L ’L JZ3 s=C fromAto C? J) - z2 B. ‘L’WWV\? M )’/- 617 ¢ |C A pendulum takes 10 seconds to complete 2 cycles. pran A A) What is its period? 5 5T < C w1 If the spring moves 10 cm from C B) What is its frequency? : ; to A (side to side), how big is it’s F I 7 = T amplitude? T i i g = g Position vs. Time Position vs. Time 80a E 1 D M 6 )@ M Lot 4] Pl {1 - A r AR i 7 ES N T I T /T [ 17 = \ T : o 3O HFEIOHO LA AT N A TN 32 s \ N1/ N \ [/ \ [/ o T T | L - c G X g \*/ g g 2 2 = g e bW -3 & v 5 oA & a3 I P A - - I SN . o al (e qar (&) o w Time {sec) Time (sec) 1 cycleafter Ais £ ; 2 cycles after D is L 1/2 cycle after G is L; 1/4 cycle before M is _L- . # of complete cycles shown is 3 . Period (T) = )5—{',& Frequency () = 1— = s 1 H% Equilibrium position = 0 Amplitude (A) = é g Mark 1 cycle of the harmonic motion. Starting at 1.5 secs, when does the 2nd cycle end: q'S 5ec Number of cycles shown is 7 -7 ¢ ke H Period (T)= %5¢(- Frequency = ~r ; =733 Equilibrium position = ] Lim Amplitude ()= 2 ¢hn) cstephenmurray.com Copyright © 2007, C. Stephen Mitrray

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