wave speed always stays constant in the same medium.

why at constant speed?

acceleration perpendicular to velocity

why circular path?

perpendicular to velocity-> centripetal force-> circular

C1

Special note

regarding motion of one point in a wave (==remember to distinguish the type!==): - mechanical waves(rope): moves only vertically - longitudinal waves(sound): moves only horizontally

a spring doing SHM: spring constant \(k\) must be constant throughout oscillation

Concepts

travelling wave: transmission of energy through vibration/oscillation of medium

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equilibrium position period/frequency/angular frequency amplitude (max displacement)

simple harmonic motion: acceleration is proportional to and opposite to the displacement characteristics: - period does not depend on amplitude - period and amplitude stays constant as time goes on

displacement-time graphs: variation of displacement of a particle over time the look of acceleration-time graph and velocity-time graph acceleration-displacement graph

phase difference(special formula) - same frequency, then \(\phi = 2 \pi \times \frac{\Delta t}{T_\text{period}}\), where \(\Delta t\) is the time difference between the nearest climax/trough of the two waves

change in kinetic and potential energy in SHM

C2

mechanical wave: A mechanical wave is a disturbance that travels in a medium through oscillations of the particles of the medium. A wave transfers energy and momentum. The direction of propagation of the wave is the direction of energy transfer.

The speed of a wave is determined only by the properties of the medium and not on how the wave is produced.

A wave is transverse if the displacement of the particles of the medium is at right angles to the direction of energy transfer. e.g. EM waves

A wave is longitudinal if the displacement is parallel to the direction of energy transfer. - compression and rarefaction

==common example of these two waves==

You cannot tell whether a wave is transverse or longitudinal by looking at displacement–distance or displacement–time graphs. The graphs look the same for both.

phase difference special formula

electromagnetic waves:

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C3

wavefronts and rays

reflection and law of reflection

refraction(air angle bigger, higher velocity, bigger angle) (Snell’s law)

total internal reflection, its requirement: - larger than critical angle - light travel from medium with higher refractive index (e.g. water to air)

principle of superposition

reflection of pulses on fixed end and free end:, to memorize: - Newton 3rd law: the wave exerts a upward force on the fixed wall, the fixed wall then gives a downward interaction force to the wave, therefore the opposite displacement - free end, free me, as I am

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diffraction

double-source interference - path difference (difference in distance of the point from the two sources) - constructive/destructive intererference

for formula \(s=\frac{\lambda D}{d}\): - \(s\) is the ==distance between nearby maxima&maxima or minima&minima!==

coherent waves: wave with same frequency(same wavelength) and constant phase difference

C4 standing wave

special note

In open space: standing wave forms as long as: - there is a wall and wave emitter - emitted wave and reflected wave travel in opposite direction

For electromagnetic wave(EM wave), since the wave speed is always the same (typically \(c\)) and ==the frequency is often fixed (like microwave in oven)==, if standing wave is formed, \(\lambda\) of the formed standing wave is the same as the original wave’s \(\lambda\), that is: \[ \lambda_{\text{micro-wave}}=\lambda_{\text{standing-wave}}=2\times\text{distance between adjacent antinodes or nodes} \]

==refraction angle（折射角） cannot be zero==, unless the incident angle（入射角） is zero

==Determine the n-th harmonic==: - both fixed/open: \(\text{anti-node number}\) - one open one fixed: \(2\times \text{anti-node number}-1\)

concepts

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standing wave: two waves of same speed, wavelength, and amplitude travelling in opposite directions meet - superposition, sum of the displacements of the two travelling waves

on a standing wave: - nodes: points having zero displacements - antinodes: points having largest displacements - the crests and troughs do not move - the amplitude of oscillation is different at different points - does not transfer energy

n-th harmonic (special formula)

how molecules move in a longitudinal standing wave (in a pipe)

open end = antinodes ; closed end = nodes

damping, natural frequency, driven frequency

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C5

Doppler Effect: change in observed frequency of a wave when there is relative motion between the source and the observer

doppler effect states the frequency change only depends on the relative velocity/motion, so it remains constant if the relative velocity is constant

blue-shift and red-shift

==when toward observer, consider velocity as positive!==

Patches

when transmit between mediums, energy loss because of partial reflection and refraction折射, so amplitude drops