L24 傳輸波 Travelling Waves


Pre-Amble

http://freewallsource.com/img/2014/9/ocean-waves-wallpaper-16832-17547-hd-wallpapers.jpg

耶和華在高處大有能力,勝過諸水的響聲,洋海的大浪。(Ps93#4)

  1. 好消息 News: Test Results for MS#3 (see previous lecture)
  2. The Link: RotationOscillationWaves (PHeT)
  3. What is a Wave? (15')

Key Ideas

Wave Speed (≠ Speed of Particles in Medium)
$$ \, v_{w,string}= \sqrt { T_s \over \mu } \, $$ $$ \, v_{w,light} = \sqrt { 1 \over \mu \epsilon } = { c \over n } \, $$ $$ \, v_{w,sound} = \sqrt { K_s \over \rho } \, $$
Special Case: SHM → Sinusoidal Waves
$$ D(\vec r,t) = A \, \sin ( \,+ \vec k \cdot \vec r \, - \, \omega t \, + \, \phi_o ) \, (positive \, direction) \,$$
$$ D(\vec r,t) = A \, \sin ( \,+ \vec k \cdot \vec r \, + \, \omega t \, + \, \phi_o ) \, (negative \, direction) \,$$
$$ \, \lambda ={ v_{w} \over f } \,\,\,\, \, \omega = | k | \, v_{w} $$ $$ \, | k |= {2 \pi \over \lambda} \, $$ $$ \, \omega = { 2 \pi f } = { 2 \pi \over T } \, $$

Doppler Effect on Frequency (medium)
$$ \, {f_r} = \left ( {{ v+ v_r } \over {v - v_s}} \right ) {f_s} \, $$
v: speed of waves in the medium (equation above)
vr: speed of receiver wrt medium; +ve (-ve) for receiver moving towards (away from) the source
vs: speed of the source wrt medium; +ve (-ve) for source moving towards (away from) the receiver
EM/light (no medium): Relativistic_Doppler_effect

ViewGraphs: Knight Chapter 20 Travelling Waves (103-1: end slide 23; 104-1: end slide 55)

Wave on a String
Rotation-Oscillation
Waves On String
Sound
Sound Waves
and Doppler
Doppler Shift Demonstrator
Doppler Shift

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