Waves! Big and small...

Transcription

1 Waves! Big and small... Wave phenomena Standing waves and music (there will be a quiz!) 1

2 Announcements! Your up-to-date clicker scores have been posted last Friday, in the Catalyst gradebook. Some scores (about 7 or 8) have not been posted, this will be updated today! 1 clicker question today at the end of the lecture Updated is schedule available online now. 2

3 Some points on Term Paper (repeated) Grading criteria: Tips: A. above average effort (exceeded minimum assignment), AND successfully carried out (facts correct, sources properly cited, communicated well, originality) B. average effort, average success OR above average effort but not entirely successful C. below average effort, OR average effort but not successful D. insultingly little effort, or drastically poor results (see for more detailed rubric) Proofread! Never turn in a paper without checking spelling, typos, etc. (And: put your name on the paper, and clip the pages together, for goodness sake!) ALWAYS cite your sources. To do otherwise is plagiarism. Don't rely on solely wikipedia or other non-academic sources: information can be wrong! Check multiple sources.

4 Waves Many physical phenomena involve wave motion ripples on a rope compression waves in a slinky water waves on the ocean sound waves in the air electromagnetic waves in space Actually, quantum theory says everything is a wave, at times But more on that later... Here we go again: first step is to describe many different kinds of waves, in unified and unambiguous terms Example: wave on a rope Take a snapshot, or... watch it move past you 4

5 Wave terminology Wavelength l = length of one full cycle (distance between peaks) Amplitude A = maximum displacement (height) Here is a snapshot of a wave with l = 1 meter, and A = 2 meters We could also say A is "4 meters peak-to-peak " 2 l = 1 m snapshot = picture of rope, frozen at one instant of time: configuration in space at a fixed point in time A = 2 m Distance, meters 5

6 Space and time pictures of waves Previous picture was "snapshot" of wave (at one instant of time) We could also stand at one place and watch wave move past us vs time Space and time pictures look similar, but we use slightly different terms: Period T = time for one cycle ("wavelength" in time units) Frequency f = cycles per second (hertz, Hz) = 1/T This wave has 6 cycles in 100 millisec, so T = s / 6 cycles = s So frequency is f = 1/T = 1/0.016s = 60 cycles/s (60 Hz) Amplitude is 170 volts*: this is the electrical signal on your house wiring! Volts AC/DC: voltage vs time time, millisec A = 170 V T = s, f = 60 Hz variation with time at a fixed point in space * We call this 120V AC, which is the RMS= Root-Mean-Square V, not the amplitude, on your house voltage. 6

7 Speed of wave, frequency and wavelength Wave speed connects the space and time pictures of wave motion Different kinds of waves move (propagate) with different speeds Speed determines relationship between wavelength (from snapshot at one t) and period or frequency (from counting waves at one spot) Relationship between frequency, speed and wavelength: f l = v f is frequency in cycles per second (Hz) l is wavelength (meters) v is speed of propagation of wave (m/s) So, for example (do simple algebra on equation above): What is wavelength of signal from KPLU-FM (88.5 MHz) l = v /f = (speed of light)/88,500,000 Hz = (3x10 8 m/s) / (8.85x10 7 cycles/s) = 3.4 m 7

8 Space, time and waves Waves move in both space and time: Wave = repetitive disturbance that propagates in space Waves on rope, water = displacements of material Sound waves, wave on slinky spring = compression waves alternating higher and lower density of material These waves propagate in a material medium (water, rope, air, spring) Light waves = changes in electric and magnetic fields (?? Later!) So: what is the medium in which light waves are disturbances? Luminiferous ether : massless substance that fills all space (?) Important implication: coordinate system in which ether is at rest is the fundamental coordinate system of the Universe!! If so, Earth's motion through ether should cause light speed to change A. Michelson, c.1890: no difference in light speed in any direction His measurements were far too good to dismiss: there is no ether Electromagnetic waves needno medium! 8

9 FYI: Water waves Surf is caused by interaction of surface waves with beach In deep ocean, waves have small amplitude At shore, their amplitude gets larger kingfish.coastal.edu/physics/projects/2001_spring/molnar/oceanofw.htm Near shore, friction with bottom slows wave so: l gets shorter (l=v/f; f=constant) A gets bigger: waves break Water inside waves moves in circles Motion only near surface Submarines do not notice storms!

10 Sound waves Sound = compression wave in material medium (air, water, iron) Sound speed depends on material properties and density (so, temperature, humidity etc) Q: what s a decibel? Decibels are used to describe any ratio on a logarithmic scale: db = 20 log 10 (A/A 0 ) For sound levels, we use the threshold of hearing as the reference level A 0 : A 0 = tiniest sound avg. person can hear For sound 10X as loud, A/A 0 =10, and log(a/a 0 )=1, so 20log(A/A 0 )=20dB A sound 1000X as loud = 60 db, etc Threshold of pain =120 db (=10 6 A 0 ) Material Air 343 Helium 972 Fresh Water 1493 Seawater 1533 Iron 5130 Diamond Sound speed, m/s

11 Waves: Interference and standing waves If I wiggle the rope at jus the right frequency Waves reflected from the end interfere with new waves I am making Interference = adding up effects of overlapping waves Constructive: waves reinforce each other; destructive: they oppose Result: looks as if some points stand still: standing waves Example of resonance: rope length L = multiple of l/2 Anti-node Point A moves with big amplitude Point B has amplitude ~0 Node Nodes = stationary points; anti-nodes=maxima Same thing happens in musical instruments Structure favors waves which have L = multiple of l/2 11

12 Guitar strings We can excite waves by plucking a guitar string Fixed ends of strings must be nodes Waves with l such that L = multiple of l/2 are reinforced (resonate) L = l/2, 2(l/2), 3(l/2) all work: harmonics What determines l? Speed of wave on string depends on: Tension in string (force stretching it) Taut = higher speed, slack = lower speed Mass per unit length of string material Heavy string = slower speed, light string = faster 12

13 Organ pipes Organ pipes have one closed and one open end Closed end must be a node, open end must be anti-node So L must be multiple of half of l/2: L=N(l/4) But if N=even number, we d get two nodes: so N = odd # only! Closed Open So resonant harmonics are L=l/4, 3l/4, 5l/4 (1 st, 3 rd, 5 th ) Imitate organ-pipe operation by blowing across end of a bottle Put water in bottle to change fundamental frequency Brass and woodwind instruments work like organ pipes Use valves to change effective length (brass), or impose an antinode somewhere inside (woodwinds) Some folk flutes (panpipes, Asian flutes) have 2 open ends: both ends are antinodes, so frequencies are same as in guitar strings. 13

14 Light waves: visible E-M waves First modern work by Newton, who considered light to be corpuscular a flow of particles Newton (via prisms) showed white light is composed of all the colors of the rainbow Newton s Optiks (1704) was the first significant treatment of the nature of light, based on an empirical (experiment-based) approach. (Book included the first published description of calculus) Despite experimental evidence for a wave nature to light, Newton s opinion on the matter damped enthusiasm for waves for 100 years Thomas Young in England, A. Fresnel and D. Arago in France, all advocated wave theory of light and proved it true via interference demonstrations Only waves can show interference effects! 14

15 Clicker question! #8 A traveling periodic wave passes a point of observation. At this point, the time between successive crests is 0.2s. What can be said about this wave? A. The wavelength is 5 m B. The frequency is 5 Hz C. The velocity of propagation is 5 m/s D. The wavelength is 0.2 m E. The period is 0.4 s