1. Types of Waves (1) Mechanical waves and electromagnetic waves
Some waves require a material substance called a medium through which to travel. Waves like this are called mechanical waves.
Examples: water waves, sound waves and seismic waves etc.
Electromagnetic waves require no medium through which to travel.
Example: radio waves, microwaves and light etc.

2. Type of Waves (2) Transverse waves and longitudinal waves
In transverse wave, the direction in which the disturbances take place is at right angles to the direction of propagation of the waves.
In longitudinal wave, the disturbances take place in a direction parallel to the direction of propagation of the waves.

3. Type of Waves (3) Progressive waves and stationary waves
A wave which transmits energy from the source to the space surrounding the source is called a progressive wave (travelling waves).
In certain conditions, waves energy is localized. When this happens, the waves are called stationary waves (standing waves).

4. Comparison of stationary waves and progressive waves
Travelling waves
Waveform does not move, but has nodes at fixed places, energy is not carried away.
Waveform moves through the medium, carrying energy, but not the medium, with it.
The amplitude varies from zero at a node to maximum at an antinode.
The amplitude is the same for all particles along the wave.
All the particles between two adjacent nodes are in phase.
Over one wavelength all particles have different phases.

5. Wave Equations
In a sinusoidal wave, each particle undergoes simple harmonic motion about its equilibrium position.This gives the equation
where  = 2 f or
where k = 2π/λ

6. Variation of Displacement with Time
Graph of the equation y t T 2T A

7. Variation of displacement with distance
Graph of the equation y x λ 2λ A

8. Wave Function for a Sinusoidal wave (1)
Mathematically the variable y depends on two variables x and t. So the combined equation is or

9. Velocity of Propagation of Mechanical Waves (1)
It is usually found that the speed of a mechanical wave is affected by two factors.
One of the factors is associated with the strength of the elastic coupling between particles in the medium through which the waves travels.
The other factor is associated with the inertia of the moving particles.

10. Velocity of Propagation of Mechanical Waves (2)
Equations giving the speed of different types of wave
Transverse wave on string
Transverse ripples on a pond
Longitudinal wave on a spring
Longitudinal wave on a rod
Sound wave in a gas

11. Huygens’ Principle
Every point on a wavefront can be considered as a source of tiny wavelets that spread out in the forward direction at a speed of the wave itself.
The new wavefronts is the envelop of all the wavelets – that is, the tangent to all of them.

12. Huygens’ Principle and the Law of ReflectionB vt A’ B’ vt
The angle of incidence=the angle of reflection

13. Huygens’Principle and the Law of RefractionB
v1t B’ A’ A
v2t
Sin i/sin r = v1/v2 = 1/2

14. Phase Change on Reflection (1)
Fixed end reflection
There is a phase
Change of  after reflection

15. Phase Change on Reflection (2)
A wave travelling from a less dense medium to a denser medium

16. Phase Change on Reflection (3)
Free end reflection
No phase change
occurs

17. Phase Change on Reflection (4)
A wave travelling from a denser medium to a less dense medium

18. Phase Change on Reflection (5)
Phase changes also occurs when longitudinal waves are reflected.
Fixed end
Free end
R C
R C
C R
R C

19. Uses of Reflected Waves
Radar (Radio Detection And Ranging)
Pulses of high-frequency radio waves are transmitted towards distant objects and their reflections are received between the transmitted pulse.
Sonar (Sound Navigation And Ranging)
Pulses of ultrasonic waved are transmitted towards under water objects, and their reflected pulses are detected.
Ionospheric Waves
Radio waves from the transmitter travels through air and is reflected by the ionosphere.

20. Uses of Radar Detect the presence of an object at a distance
Detect the speed of an object
Map something-to create detailed topographic maps of the surface of planets and moons.

21. Uses of Sonar Depth sounders Fish finders Side Scan sonar
To measure the depth of the sea
Fish finders
To detect shoals of fish
Side Scan sonar
To map the ocean floor

22. Atmospheric Windows to EM Radiation

23. Reflection of Radio Waves from the Ionosphere

24. Propagation of Radio Waves

25. Transverse waves
Particles vibrate along a line which is perpendicular to the direction of travel of the disturbance.

26. Longitudinal Waves
Particles vibrate along a line which is parallel to the direction of travel of the disturbance.
Rarefaction
Compression 

27. Stationary Waves  Nodes Antinodes
A stationary wave doesn’t appear to be travelling.
Nodes
Antinodes 