C. Wave behaviour

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2024/06/24 03:17

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C.1.1 Simple harmonic oscillations and its conditions

Oscillation: periodic motions which center around an equilibrium position

Wave: transfer of energy without transfer of matter

Simple harmonic motion (SHM): motion in which the restoring force (acceleration) is directly proportional to the displacement of the body from its equilibrium point

Period and amplitude are constant

Period is independent of amplitude

Sinusoidal (can be represented into sine or cosine graph)

C.1.1-1 2D diagrams and graphs that represents SHM in pendulum

Condition for simple harmonic motion:

A restoring force is required for simple harmonic motion to occur

Magnitude of restoring force is proportional to displacement and acts towards the equilibrium

F ∝-x, F=-kx (k=spring constant)

C.1 Simple Harmonic Motion

C.2.1 Traveling waves, wave properties, transverse and longitudinal waves

Traveling waves

continuous disturbance in a medium that travels in the direction of propagation

Energy is transferred by waves, but matter is not transferred by waves

Waves are generated by oscillating sources

Oscillations can propagate through a medium or in vacuum, depending on the type of wave

Direction of a wave is defined as the direction of the propagation of energy

continuous waves → succession of individual oscillations, wave pulse → one oscillation

C.2.1-1 Graph showing the progression of travelling wave

Types of Waves (Transverse / Longitudinal)

Real life Examples

C.3.1 Wavefronts and rays, Amplitude and Intensity

Wave characteristics and definitions

Waves can be described in terms of the motion of a wavefront and/or in terms of rays.

Wavefronts: surface joining neighboring points where oscillations are in phase with each other

Can be curves or straight lines

Always perpendicular to the direction of wave propagation

C.3.1-1 Diagram of progressing wave with notations

(distance between successive wavefronts) = (λ\lambdaλ of the wave)

C.3.1-2 Graph of transverse wave with key-terms notated

Rays: path taken by the wave energy propagation

Indicate the direction of wave propagation

Are perpendicular to wavefronts

C.3 Wave Phenomena

C.4.1 The nature of standing waves

Standing waves result from the superposition of two opposite identical waves:

Standing waves are formed when the two waves interfere with:

the same amplitude

the same frequency

traveling in opposite directions

In standing waves:

the positions of the crests and troughs do not change

energy is not transferred yet there is energy associated with it.

Nodes: the points where the total displacement always remains zero

Antinodes: the points where the displacement varies between a maximum in one direction and in the other direction

C.4.1-1 A standing wave - the pattern remains fixed

C.4.2 Boundary conditions

C.4 Standing Waves and Resonance

C.5.1 The Doppler Effect

The Doppler effect

When a source of sound, such as the whistle of a train or the siren of an ambulance, moves away from an observer :

When the observer and the source of wave are both stationary :

C.5.1-1 Diagram of doppler effect (stationary)

When the source starts to move towards the observer, the wavelength of the waves is shortened

C.5.1-2 Diagram of doppler effect (moving source)

Redshift/Blueshift of EM Radiation

In space the Doppler effect of light can be observed when spectra of distant stars and galaxies are observed, this is known as :

C.5.1-3 Diagram of redshift

Redshift : The fractional increase in wavelength due to the source and observer receding from each other

C.5 Doppler Effect