Pre-Amble
耶和華在高處大有能力，勝過諸水的響聲，洋海的大浪。(Ps93#4)
- 好消息 News: Test Results for MS#3 (see previous lecture)
- Homework: SHM (Bobble Heads)
- The Link: Rotation → Oscillation → Waves (PHeT)
- 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: Travelling Waves (Ref" Knight Chapter 16) (103-1: end slide 23; 104-1: end slide 55 108-1 to end)
- 1D Wave Description (waves on strings)
- wave speed (v)
- Lateral (⊥) ↔ Longitudinal (∥)
- Displacement D(x,t), Particle Velocity dD/dt(x=C,t)
- Sinusoidal Waves
- Nature of Sound & Light
- 2D and 3D Waves
- Power and Intensity (decibels)
- Doppler Effect (Introduce with Simulations)
