# Module 3: Waves and Thermodynamics

## Wave Properties

- Vibrating objects transfer energy through waves
- Waves are classified by what they move through
- There are two types: mechanical and electromagnetic

### Mechanical Waves

- Mechanical waves transfer energy through vibrations in a medium
- Examples include water, sound and wind
- A wave can be a single pulse, or continuous

Waves only transfer energy from one point to another. THEY DO NOT TRANSFER MATTER! However, matter may move as the wave passes through it.

Mechanical waves can be either transverse or longitudinal.

In a transverse wave, particles oscillate (move back and forth) perpendicular (at 90°) to the direction of energy transfer.

In a longitudinal wave, particles move parallel to the direction of energy transfer.

### Measuring Mechanical Waves

Waves can be represented by displacement-distance graphs and displacement-time graphs.

The graph takes a sinusoidal shape (like a sine wave)

### The Role of the Medium

- Speed of sound waves in a medium depends on 2 main factors:

- Elasticity of the medium
- Density of the medium

- The more rigid a material is, the faster the mechanical waves are transmitted
- The more elastic a material is, the slower a mechanical wave is transmitted
- The higher the temperature a given medium is, the faster a mechanical wave will move through it.

## Electromagnetic Waves

- All EM waves propagate through space at $3\times10^{8}m/s$
- EM waves do not require a medium as they self-propagate
- A charged particle produces an electric field.
- A moving charged particle produces a magnetic field.
- An oscillating charged particle produces an EM wave.
- EM waves consist of perpendicular electric and magnetic fields.

### Other Properties of EM Waves

All EM waves are transverse waves.

All able to undergo:

- Reflection
- Refraction
- Polarisation
- Interference
- Diffraction

All EM waves travel in straight lines

### Displacement-Time Graph of a Transverse Wave

- The displacement time graph of a transverse wave shows how a single particle is displaced from natural resting position as a function of time

## Wave Behaviour

### Wavefronts and Rays

- Rays refer to direction in which energy moves from initial disturbance which created the wave
- Wavefront essentially marks points at which energy of particles are equal

### Reflection

- The law of reflection state that $θ_{i}=θ_{r}\newcommand{orange}{\color{orange}}\newcommand{pink}{\color{pink}}$
- A reflected wave has the same frequency, wavelength, and speed as the incident (original) wave
- Wavefronts are identical before and after reflection

$\newcommand{orangebox}{\bbox[5px, border: 2px solid orange]}\newcommand{pinkbox}{\bbox[5px, border: 2px solid pink]}\newcommand{greenbox}{\bbox[5px, border: 2px solid green]}$

#### Convex Mirrors

- Rays diverge after reflection
- Used in car mirrors and surveillance systems

#### Concave Mirrors

- Curves inward and waves converge at the focus
- Used to reflect microwaves or radio waves from collecting dishes to receiving antenna

### Refraction

- When an EM wave travels from one medium to another some of the wave will be absorbed, some reflected, and the rest propagates through the new medium

$$\color{orange}{n_{1}\sin\left(\alpha\right)=n_{2}\sin\left(\beta\right)}$$

- Where $\alpha$ and $\beta$ are the angles from the
*normal*(the red line in the image) and n values are the refractive indices of the media- the refractive index of a material will usually be given in exams, but it is useful to remember that air is $n\approx 1,$ glass is $n\approx 1.5,$ and water is $n\approx \frac{4}{3}$
- Usually, a more dense substance will have a higher refractive index

When light moves from one medium to another:

- Frequency of light remains unchanged
- Wavelength of light changes
- Velocity of wavelength changes
- When a wave slows down, it bends
**towards the normal**

### Diffraction

- Refers to the spreading if waves as the waves passes an object or travels through a gap between objects
- Wave diffracts around barrier at edges, leaving a shadow region behind it where the wave does not reach.
- The amount of diffraction is proportional to the wavelength AND the size of the slit:

$$\orange{\text{Diffraction}=\frac{\omega}{\lambda}}$$

### Superposition

- Superposition is the overlapping of two waves
- There are two types of superposition: constructive (waves add to make a larger wave) and destructive (waves cancel each other out to make a smaller wave)
- Superposition results in a temporary change of frequency, amplitude and phase
- Once the waves have passed each other, the superposition collapses, and both waves return to their original properties

### Standing Waves

Standing waves are waves which do not appear to be moving along the medium

Instead, the

*antinodes*(peaks and troughs) seem to switch displacement twice every cycleStanding waves are frequently used in music, where:

$$\orange{\mathcal{f}_{n}=n\cdot\mathcal{f}_{1}}$$

$$\orange{\lambda_{n}=\frac{1}{n}\cdot\lambda_{1}}$$

- In other words, the frequency of harmonic n is equal to n multiplied by the frequency of harmonic 1 (usually middle C)

### Resonance

- A phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies
- Occurs at frequencies where response amplitude is a maximum is termed “resonant frequency”

## Sound Waves

- Sound is a mechanical wave; the wave is caused by a vibrating source.
- Travel as alternating regions of compressions and rarefactions.
- Travel at 343m/s
- Changes depending on air pressure and temperature

- Sound waves are measured in $W/m^2$, and are calculated by:

$$\orange{I=\frac{P}{4πr^{2}}}$$

### Frequency and Pitch

- Frequency is the quantitative equivalent of pitch

### Amplitude and Volume

- Amplitude and volume are
*directly proportional*(increasing one increases the other)

Echoes:

- Minimum distance the boundary needs to be away (from both the source and the listener) is 17m.
- The sound wave has to travel a total of at least 34m.
- The best echoes come from hard, smooth surfaces.
- For a human to perceive two sounds as separate sounds, they MUST be 0.1 seconds apart.

## The Doppler Effect

- When the source of a sound wave approaches an observer, the observer interprets the sound as compressed, and therefore higher pitched
- The opposite is true when the source is travelling away from an observer
- The frequency shift can be calculated by:

$$\orange{f\prime=f\left(\frac{v_{wave}+v_{observer}}{v_{wave}-v_{source}}\right)}$$

## Ray Model of Light

### Ray Diagrams

### Describing Ray Diagrams

Questions will often ask you to describe the image produced by a ray diagram

To describe these images, use TOMP:

**T**ype of image (real/virtual)**O**rientation (upright/inverted)**M**agnification (enlarged/diminished/true size)**P**osition (distance from the mirror)

Magnification can be calculated by:

$$\orange{M=\frac{h_{i}}{h_{o}}\text{, where:}}$$

- $M=$magnification scale
- $h_i=$ image height
- $h_{o}=$ object height

### Mirror Formula

$$\orange{\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\text{, where:}}$$

$f=$ focal length of the mirror (cm)

$u=$ distance between mirror and object (cm)

$v=$ distance between mirror and image (cm)

- Now that we have the mirror formula, we can expand the magnification formula:

$$\orange{M=\frac{h_{i}}{h_{o}}=\frac{-v}{u}}$$

### Lenses

- A lens is a transparent piece of material which bends light in a specific manner
- Converging lenses bend light rays to meet at a specific focal point
- Diverging lenses bend light away from each other

Converging Lens:

Diverging Lens:

### Refractive Index

The speed of a wave depends on the density of the medium

The density, when referring to its effect on waves, is referred to as a medium’s

*refractive index*A total vacuum has a refractive index of $n=1.00$

A higher refractive index means light will travel slower in that medium

Refractive index is calculated by:

$$\orange{n_{material}=\frac{c}{v_{material}}}$$

- Where $c$ is the speed of light in a vacuum $(3\times10^{8}\text{ m/s})$

## Thermodynamics

### Temperature and Kinetic Energy

- While an object may be at rest, the particles it is composed of are in a constant state of motion
- As temperature increases, the Kinetic energy increases, so the particles move more quickly
- This allows energy to be transferred faster at higher temperatures

Heat is a measure of the transfer of thermal energy between bodies

### Thermal Equilibrium

Thermal energy is always transferred from regions of higher temperature to regions of lower temperature

The Zeroth Law of thermodynamics states that:

“If two thermodynamics systems are each in equilibrium with a third system, then they are also in equilibrium with each other.”

The First Law of Thermodynamics, also known as the Law of Conservation of Energy, states that:

“Energy cannot be created, nor destroyed.”

### Specific Heat Capacity

A measure of how much energy 1kg of a substance must absorb to increase in temperature by $\newcommand{deg}{^{\circ}}1\deg C$

Water has a specific heat capacity of 4186J/kg/K

- In other words, it takes 4186J of energy to increase the temperature of 1kg of water by 1 Kelvin

Specific heat capacity can be calculated with the formula:

$$\orange{\Delta Q=mc\Delta T\text{, where:}}$$

- $ \Delta Q=$change in energy (Joules)
- $m=$ mass of the substance (kg)
- $c=$ specific heat capacity of the substance (J/kg/K)
- $\Delta T=$ change in temperature (K)

### Latent Heat

- Latent heat of fusion is the amount of energy required to change 1kg of a substance from liquid to gas WITHOUT CHANGING ITS TEMPERATURE

$$\orange{Q=mL\text{, where:}}$$

$Q=$ Energy released (J)

$m=$ mass of the substance (kg)

$L=$ Latent heat of fusion (J/kg)