PHYSICS TOPIC 4 - WAVES

Study Guide
4.1 Oscillations KEY CONCEPTS
Oscillations
Oscillations – they are vibrations that are in continuous motions which they repeat themselves. It
is an periodic motion

Eg. Pendulum is an example of oscillating motion.

In all oscillation, v = 0 (when it’s at peak) and vmax (at middle)

Oscillation Quantities
TIME PERIOD FREQUENCY
Period (T) – time taken to do one revolution Frequency (f) – defined as how many
Unit: seconds (s) cycles/oscillations occurs each second
Unit: Hertz (Hz)
1
𝑇= (T = Time period, f = frequency)
𝑓 1
𝑓 = 𝑇 (T = Time period, f = frequency)
DISPLACEMENT AMPLITUDE
Displacement – is the distance from a point Amplitude – the maximum distance from
to equilibrium. Zero displacement is displacement to the equilibrium position
equilibrium

Simple Harmonic Motion

SHM (Simple Harmonic Motion) – defined as an oscillation which the acceleration/restoring
force is proportional to the displacement and in the opposite direction (𝑎 ∝ −𝑥)

𝑚𝑎 = −𝑘𝑥 (m = mass in kg, a = acceleration in ms-2, k = spring constant, x = displacement)

Period and Amplitude are constant.

Phase Difference
In phase – defined as oscillations are oscillating at same time
Phase difference – oscillators that has same frequency but not in phase

Energy Changes in SHM

In SHM, there’s also continuous energy exchange. This continuous exchange occurs between
(Ek and Ep)

The sum of Ek and Ep is constant, 𝐸𝑇 = 𝐸𝑘 + 𝐸𝑝 (𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

 4.2 Travelling Waves KEY CONCEPTS
Travelling Waves
Wave – it’s a disturbance that’s travels/vibrates in a medium. It’s transfers energy and
momentum from 1 point to another

Direction of propagation of waves is the direction of energy. There’s energy transfer and no net
motion

MECHANICAL WAVES
TRANSVERSE WAVES LONGITUDINAL WAVES
The wave motion which the particles travel/vibrate The wave motion which the particles travel/vibrate
perpendicular to wave’s direction parallel to wave’s direction

Transverse waves have trough and crest (max/min Longitudinal waves has compression (squishing particles
displacement) in an area) and rarefaction (separating the molecules in
an area)

Wave Components
TIME PERIOD FREQUENCY
Period (T) – time taken to do one revolution Frequency (f) – defined as how many
Unit: seconds (s) cycles/oscillations occurs each second
Unit: Hertz (Hz)
1
𝑇= (T = Time period, f = frequency)
𝑓 1
𝑓 = 𝑇 (T = Time period, f = frequency)
DISPLACEMENT AMPLITUDE
Displacement – is the distance from a point to a Amplitude – the maximum distance from displacement
equilibrium. Zero displacement is equilibrium to the equilibrium position

WAVELENGTH
Wavelength () - the distance from trough-trough/crest-
crest

𝜆
𝑣=
𝑇
𝑣 = 𝜆𝑓

v = velocity in ms-1,  = wavelength in m

f = frequency in Hz
Electromagnetic Waves
Electromagnetic Waves – waves that travel with the speed of 𝑣 = 3 × 108 𝑚/𝑠
Electromagnetic waves exist only in transverse waves

In free space, electromagnetic waves doesn’t need a medium for which it to travel.

𝑐 = 𝜆𝑓 (c = speed of light,  = wavelength in m

f = frequency in Hz)

In electromagnetic waves, it also follows

SHM that has oscillating Electric and
Magnetic fields (perpendicular to each
other)

Electromagnetic Spectrum
4.3 Waves Characteristics KEY CONCEPTS
Wavefronts & Rays
Wavefront – a line/place which the wave vibration on every point is same (vibrate
in-phase)
They don’t have to be straight, they can travel spherically

Rays – lines which indicate the direction to wavefronts. Rays are perpendicular to
wavefronts

Amplitude & Intensity

Intensity – the rate of energy being transmitted per unit area
𝑃 𝑃
𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 = 𝐴 = 4𝜋𝑟2 (I = intensity, P = power, A = surface area) Units: Wm-2

Intensity is proportional to amplitude and inversely proportional to distance. The farther you
1 𝐼 𝑥2
move from sound source, less the intensity (𝐼 ∝ 𝐴2 , 𝐼 ∝ 𝑥 2), 𝐼2 = (𝑥1)2
1

Superposition
Superposition – the addition/sum of waves simultaneously
passing through the medium

Constructive interference: Sum of 2 or more waves (in-phase)

Destructive interference: Sum of 2 or more waves (out of phase
– cancel out)

Polarization
Light is a transverse wave (polarization only occur to transverse waves).
Light polarization is oscillation of electric fields

Unpolarized light – light that’s randomly oriented in many directions

Polarization – light that’s only being absorbed oriented in 1 direction
only

Malus’s law: 𝐼 = 𝐼0 𝑐𝑜𝑠 2 𝜃 (Malus law relates to incident intensity and transmitted intensity of
light passing through a pola rizer and an analyzer) 𝐼 ∝ (𝐼0 𝑐𝑜𝑠 2 𝜃)
Light intensity is reduced by half when light passes through a polarizer (analyzer)

Polarization by reflection/refraction
When light is transmitted across a boundary between two mediums with different refractive
indexes, part of the light is reflected and the remaining part is refracted

If the refracted and reflected rays make a 90° angle then the reflected ray will be totally linearly
polarized. θrefl +θrefr = 90° (or θinc +θrefr = 90°)
𝑛
tanθ = 𝑛2 (Used for calculating incident angle).
1
It depends on the refractive index and the 2 mediums
4.4 Wave Behaviour KEY CONCEPTS
Reflection
Reflection – occurs when a wave meets a boundary or there’s change in medium. Resulting
waves are reflected (diverted backward)

Law of reflection:
• Incident ray and refracted ray are separated by a normal line.
Rays and normal line lie on same plane
• Angle of incidence  = Angle reflected 

Refraction
Refraction – the phenomenon when waves are bent on the surface and
changes the direction of the wave

Waves moves from denser region and arrive at the boundary with less
denser medium
Incident ray is faster than refracted ray (Refracted ray speed is lower than
incident ray). Speed and wavelength changes

𝑆𝑛𝑒𝑙𝑙 ′ 𝑠 𝑙𝑎𝑤 𝑜𝑓 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦: 𝑣1 sinθ1 = 𝑣2 sinθ2 (v – wave velocity in ms-1, 

- wave angle)

Refractive index
Refractive index – defined as the ratio of speed of light in the vacuum to the speed of light in
the medium
𝑐
𝑛 = 𝑣 (n – refractive index, c = 3 x 108 m/s, v – velocity in medium)
𝑆𝑛𝑒𝑙𝑙 ′ 𝑠 𝑙𝑎𝑤 𝑜𝑓 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥: 𝑛sinθ1 = 𝑛2 sinθ2

Waves move from optically dense region to region with less dense region (possible for the light
to be reflected – total internal reflection)
Critical Angle – the angle of incident ray equal to the angle of
refraction. It occurs when the refracted angle is 90 (c = 90)

Total internal reflection - occurs when the light ray propagates

from a optically denser medium to an optically less dense
medium.
𝑛2
sin𝜃𝑐 = (c = critical angle, n = refractive index)
𝑛1
n should be greater than 1
Diffraction
Diffraction – the phenomenon when waves are bent
through a process. It is caused by objects that interacts
with the waves

Huygens principle - Every point on a wavefront emits

a spherical wavelet of the same velocity and
wavelength as the original wave.
This is because that waves can turn corner. Waves can
also interfere with other waves

Double slit interference

Double slit interference – when 2 wavelets interfere with each other (in-phase and same
frequency)
Coherent waves – waves that vibrate at same rate having a constant/in-phase relationship

Path difference – the difference in the distance travelled by 2 waves from the source point
𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑣𝑒 𝐼𝑛𝑡𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑛𝜆
1
𝐷𝑒𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑣𝑒 𝐼𝑛𝑡𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (𝑛 + )𝜆
2
where n represents the integer.

Central maximum (the distance travelled by waves is equal – constructive interference)

Minimum (the distance travelled is halved – destructive interference)

𝜆𝐷
𝑠= (s – fringe spacing,  - wavelength, D – screen to slit distance, d – slit spacing)
𝑑
Width and brightness of interference strip pattern are uniformly spread out in the screen
• White/brightness of fringe (constructive interference)
• Black/dark of fringes (destructive interference)
 4.5 Standing Waves KEY CONCEPTS
Standing Waves
The principle of superposition yields the sum of 2 opposite travelling waves. 2 opposite waves
travel and does superposition

Standing wave – the resultant wave that doesn’t

travel/vibrate.
Standing waves vibrate up and down rather than travelling left
and right

Nodes and Anti-node

The standing wave’s lobes grow up and down

Node – any point in standing wave that has zero displacement

Antinode – any point where the lobes grow/shrink

Harmonic Patterns
Fundamental frequency – lowest frequency that we can get from
half wavelength (1st harmonic)
𝑣
𝐹𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = (v – velocity, L – length)
2𝐿

Every subsequent harmonic follows with additional half wavelength

(as well as 1 node and 1 antinode)
2𝐿 4𝐿
𝑛𝑡ℎ ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐: 𝑛 𝑜𝑟 𝑛 (n – integer of harmonic, L – length)

Boundary Conditions
STRINGS CLOSED PIPES
For stringed instrument, transverse waves travel to the For pipes, longitudinal waves travel to each end and
ends of the string and reflect at each end reflected from 1 side
Fixed end (2 nodes) and open space (anti-node) Closed end (node) and open end (anti-node)

1 closed end & 1 open end (odd harmonics)

2 open ends (any harmonic)

Standing VS Travelling Waves