Physics 116 Lecture 5 Waves Oct 6, 2011 R. J. Wilkes Email: - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Lecture 5

Waves

Oct 6, 2011

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Today

Lecture Schedule

(up to exam 1)

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4

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

• scillations

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5

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 5 Physics 116

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• 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: wave on a rope watch it move

past you

Take a

snapshot, or...

Waves

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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

• 2
• 1

1 2 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Distance, meters

T= 1 s

A = 2 m

7

Space and time pictures of waves

time, seconds (Here: period T=1sec)

variation with time at a fixed point in space

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• 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)
• 2
• 1

1 2 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Distance, meters

λ = 1 m

A = 2 m snapshot = picture of rope, frozen at one instant of time: configuration in space at a fixed point in time

At one instant: a snapshot in time

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(Here: wavelength λ =1 m)

9

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 = (3x108 m/s) / (8.85x107 cycles/s) = 3.4 m

Speed of wave, frequency, and wavelength

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• 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)
• Sound speed depends on material properties and density (so,

temperature, humidity etc)

www.kettering.edu/~drussell/Demos/waves/wavemotion.html

Longitudinal waves

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• 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 have no medium

Q: then, what is the rest frame of the Universe?

Kinds of waves

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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

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• 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 – Amplitude A gets bigger near shore: water piles up, and waves break

Water waves

v gD =

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Example

• Typical surf has period 10 sec and λ = 150m

What is wave speed?

• Tsunami (tidal wave) moves with speed 750 km/hr and

wavelength 310 km in mid-ocean, where depth is 5000 m What is its frequency?

• 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 – All the water in a shallow wave 310 km long gets piled up into 15 km wave

( )

4

750 km/h 1 h 6.7 10 Hz 310 km 3600 s v f λ

−

⎛ ⎞ = = = × ⎜ ⎟ ⎝ ⎠ 1 150 m 15 m / s 10 s f v λ ⎛ ⎞ = = = ⎜ ⎟ ⎝ ⎠

( )(

)

2 4 4

9.8 / 10 10 / 10 / 6.7 10 Hz 15 km 6.7 10 Hz v gD m s m m s v m s for f f λ

− −

= = ≈ ⎛ ⎞ = × → = = = ⎜ ⎟ × ⎝ ⎠

Deep water shore

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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

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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

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