Physics 116 Lecture 5 Waves Oct 6, 2011 R. J. Wilkes Email: ph116@u.washington.edu
Announcements • Homework 1 is due TODAY by 5 pm! • Webassign says: their site will be down for maintenance Saturday, 3am to 9am • Go-Post discussion board for 116 is open now
Lecture Schedule (up to exam 1) Today 10/6/11 Physics 116 3
Driven oscillations and resonance • Any system that displays SHM has natural frequency = f when it is displaced once and left alone • Driven oscillator has external agent displacing it with some period (not necessarily same as its natural T) • If driving force has same f as system’s natural f, energy gets transferred into the system very efficiently – Often disastrously, if undamped! – This is called resonance resonant frequency = natural f Tacoma Narrows bridge, 1940: Classic example of driven oscillations 10/6/11 Physics 116 4 4
Tacoma bridge collapse • First Tacoma Narrows bridge (“Galloping Gertie”) – Construction started September,1938 (WPA funded: 6.4 M$!) – Opened July 1, 1940 – Collapsed November 7, 1940 • Videos: http://www.youtube.com/watch?v=P0Fi1VcbpAI (more detail: http://www.youtube.com/watch?v=j-zczJXSxnw ) Cause of failure: (see http://www.wsdot.wa.gov/tnbhistory/Machine/machine3.htm) • Vibration was due to aeroelastic torsional fluttering – Wind injects more energy than the flexing of the structure can dissipate: damping is ineffective, exponential increase in A – Occurs even with relatively low-speed, steady winds • Flutter velocity = wind speed at which fluttering begins – Now designers make sure flutter v >> max expected wind v ! • Interesting example of physics misinformation: textbooks say – “Due to resonance” – Driven by “vortex shedding” Karman vortex shedding: Air density behind a cylinder as air blows over it 10/6/11 Physics 116 5 5
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 – Light waves in intergalactic space • Actually, quantum theory says everything is a wave, sometimes – more on that later... • As before: first step is to describe many different kinds of waves, in unified and unambiguous terms Example: Take a wave on a rope watch it move snapshot , or... past you 6 10/6/11 Physics 116
Space and time pictures of waves We’ve been through this already with oscillations… • We could stand at one place and watch wave move past us vs time • Graph of displacement vs time • Period T = time for one cycle ("wavelength" in time units) to go past • Frequency f = cycles passing per second (hertz, Hz) = 1/T – This wave has 1 cycle in 1 s, so T = 1 s – Amplitude is 2 meters T= 1 s 2 variation with 1 time at a fixed point in space 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 A = 2 m -1 -2 time, seconds Distance, meters (Here: period T=1sec) 10/6/11 Physics 116 7
At one instant: a snapshot in time • Previous picture was graph of displacement vs time at one location • Here: Picture of rope at one instant of time (say, t=0): – We see rope’s displacement vs position along rope (y vs x) Wavelength λ = length of one full cycle (distance between peaks) • • Amplitude A = maximum displacement (height) λ = 1 m 2 snapshot = 1 picture of rope, frozen at one 0 instant of time: 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 A = 2 m configuration -1 in space at a fixed point in -2 time (Here: wavelength λ =1 m) Distance, meters 10/6/11 Physics 116 8
Speed of wave, frequency, and wavelength Wave speed connects the space and time pictures of wave motion • Different kinds of waves move (propagate) with varying speeds – Speed determines relationship between wavelength (from snapshot at one t) and period or frequency (counting waves at one spot) • Relationship between frequency, speed and wavelength: f · λ = v f is frequency in cycles per second (Hz) λ is wavelength (meters) v is speed of propagation of wave (m/s) So, for example What is wavelength of signal from KPLU-FM (88.5 MHz) λ = v / f = (speed of light)/88,500,000 Hz = (3x10 8 m/s) / (8.85x10 7 cycles/s) = 3.4 m 10/6/11 Physics 116 9
Longitudinal waves • Sound waves are an example of longitudinal waves – Disturbance consists of periodic changes in density of the medium – At any point, material is alternately compressed and rarified – Compression peaks propagate through the medium • Sound = compression wave in material medium (air, water, iron) www.kettering.edu/~drussell/Demos/waves/wavemotion.html • Sound speed depends on material properties and density (so, temperature, humidity etc) 10/6/11 Physics 116 10
Kinds of waves • Waves move in both space and time: – Wave = repetitive disturbance that propagates in space • Transverse waves: on rope = displacements of material • Longitudinal waves: sound, slinky = compression of material These waves propagate in a material medium (water, rope, air, spring) • Light waves = changes in electric and magnetic fields – Is there a 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, 1890s: no difference in light speed in any direction – Measurements were far too good to dismiss: there is no ether Electromagnetic waves Q: then, what is the rest have no medium frame of the Universe? 10/6/11 Physics 116 11
Waves in water • Waves on water (or any surface) are a special case • Water inside waves moves in circles – Motion only near surface – Submarines do not notice storms! – Imagine we can make a video of “particles of water” www.kettering.edu/~drussell/Demos/waves/wavemotion.html 10/6/11 Physics 116 12 12
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: – λ gets shorter (because f remains constant: λ = v/f) = – shallow-water speed (for depth D in m) is approximately v gD – Amplitude A gets bigger near shore: water piles up, and waves break 10/6/11 Physics 116 13
Example Typical surf has period 10 sec and λ = 150m Deep water shore • ⎛ ⎞ What is wave speed? 1 λ = = = ⎜ ⎟ f v 150 m 15 m / s ⎝ ⎠ 10 s • Tsunami (tidal wave) moves with speed 750 km/hr and wavelength 310 km in mid-ocean, where depth is 5000 m ( ) ⎛ ⎞ 750 km/h What is its frequency? v 1 h = = = × − 4 ⎜ ⎟ f 6.7 10 Hz λ ⎝ ⎠ 310 km 3600 s • If it reaches shallow water near shore, its frequency stays the same but its speed gets slower, and λ gets shorter: – Near shore where water is 10m deep, Tsunami described above has speed ( ) ( ) = = ≈ 2 v gD 9.8 m s / 10 m 10 m s / ⎛ ⎞ v 10 m s / − = × → λ = = = 4 6.7 10 Hz ⎜ ⎟ 15 km for f × − ⎝ ⎠ 4 f 6.7 10 Hz – All the water in a shallow wave 310 km long gets piled up into 15 km wave 10/6/11 Physics 116 14 14
Clicker channel programming Clicker channel programming • Press and hold down-arrow • When light flashes, press 02 (zero, then 2) • When light flashes again, press down- arrow
Pop quiz # 1 • We’ll wait 2 minutes for everyone to answer each question 3. Which of the following is an example of a transverse wave? A. Sound wave in air B. Water waves at Waikiki Beach C. Wave on a plucked guitar string 10/6/11 Physics 116 16 16
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