Waves

Waves: The transfer of energy from one place to another without the net displacement of matter
- I.e. after energy is transferred, there is no displacement of matter
Mechanical waves: transfer energy from one place to another without the net displacement of matter, but requires a medium to propagate
- The particles in the medium vibrate back and forth about fixed positions (equilibrium position)
Transverse waves: particles vibrate perpendicular to the direction of energy flow, e.g. water, electromagnetic waves
Longitudinal waves: particles vibrate along straight lines parallel to the direction of the energy flow
However:
1. Assumes no other disturbances in the motion
2. Ignores situations where there is no medium
Requirements for medium:
1. Mechanical waves must have a medium, e.g. sound
2. Non-mechanical waves do not require a medium, e.g. EMR

Anatomy of a Wave

Crest: Highest displacement of a particle in the positive direction
- Highest point in the graph
Trough: Lowest displacement of a particle in the negative direction
- Lowest point in the graph
Wavelength ( $λ$ ): Distance between any 2 consecutive points in a wave that are in phase
- From one crest to another crest
- From one trough to another trough
- Distance it takes for the wave to repeat
Frequency (f): The number of complete oscillations per second. Unit of frequency is the Hz(Hertz)
- Remains constant, even if reflected/refracted
- Frequency and wavelength are inversely proportional to one another
Period (T): Time take for one wavelength to complete (seconds), equal to $\frac{1}{f}$
Phase: State of vibration that a particle has reached in its cycle of motion. Waves are in phase when particles of the wave move in the exact same way at the same time
Speed = distance/time
Distance = speed $\times$ time
Time = distance/speed $v = f λ = \frac{λ}{T}$
Speed of sound at $25˚ C$ is $346$ $m s^{- 1}$
$f$ remains constant, thus if $v$ increases, $λ$ increases

Energy incident upon a surface is
- Reflected
- Absorbed
- Transmitted (goes through the object)
- Usually a combination of these 3

When energy is incident upon a surface (e.g. boundary between 2 different mediums), then some/all of the energy “bounces” back into the original medium

Occurs when a wave passes from the medium to another, at an angle other than 90˚ and changes direction
Changes speed, and therefore wavelength, but not frequency
NB: The media may simply be referred to as slow(er) or fast(er)
We all know that in order of density, solid > liquid > air > vacuum
- Sound: speed of sound increases with density of medium
- Light: speed of light decreases with density of medium
  - If a ray goes into a slower medium it bends towards the normal

Bending/spreading of waves beyond a gap/slit/aperture with no change in wavelength, frequency or velocity
Diffraction around corners
- When a wave moves past a corner, due to the wavefront being a source of secondary wavelets; the wave diffracts and spreads out.
- The area where there is no diffraction is called the shadow region
Wavelength Effect
- Diffraction increases with increase in wavelength.
- Thus long wavelength (low frequency) waves are diffracted more than short wavelength (high frequency) waves
- This is why ultrasound waves don’t diffract much and are used for locating purposes such as in sonar or ultrasound; they do not disperse/diffract much at all.
Aperture Size Effect
- As the aperture size increases, the extent of diffraction decreases.
- As the aperture Size decreases, the extent of diffraction increases
- The diffraction is greater when wavelength size is roughly equal to the aperture size
- For apertures smaller than the wavelength size, there is no diffraction

$I = \frac{P}{A} = \frac{\frac{W}{t}}{A} = \frac{W}{A t}$

Intensity is known to decrease by the inverse square law of waves as they spread in ALL directions

$I \propto \frac{1}{l e n g t h ^{2}}$

$\frac{I _{1}}{I _{2}} = \frac{( R _{1} ) ^{2}}{( R _{2} ) ^{2}}$