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.

      Longitudinal and Transverse Waves

  • This simulation demonstrates a wave - PHET COLORADO

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:
  1. Elasticity of the medium
  2. 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 Graph

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


  • 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


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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


  • 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



  • 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
If the boundary is struck parallel to the normal, the wavelength and speed still change, but the direction does not.


  • 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:




  • 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 cycle

  • Standing waves are frequently used in music, where:



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



  • 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:


Frequency and Pitch

  • Frequency is the quantitative equivalent of pitch

Amplitude and Volume

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


  • 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:


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:

    • Type of image (real/virtual)
    • Orientation (upright/inverted)
    • Magnification (enlarged/diminished/true size)
    • Position (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)

The formula for lenses is the same, just switch out “mirror” for “lens”
  • Now that we have the mirror formula, we can expand the magnification formula:



  • 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:


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


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)

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