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WAVES

Waves - oscillations that carry energy; alternatively, disturbances produced in a medium to create energy

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Medium - substances that make possible the transfer of energy from one location to the other, predominantly through waves

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There are several types of waves, e.g. electromagnetic waves and sound waves. EM waves include visible light waves, which allow us to see objects around us. Different waves also travel using different mediums - sound waves require matter to travel through, whereas EM waves can also travel in a vacuum and require no medium at all.​

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Mechanical waves - waves that require a medium, be it a fluid, solid, or otherwise, to transmit energy

WAVE PHENOMENA

Waves undergo a variety of reactions when travelling in various mediums, or when faced with an obstacle. This is because waves won't simply stop once they encounter a different medium, or  meet an obstacle.

 

The most common behavior of waves are as follows:

  • Reflection

  • Refraction

  • Diffraction

  • Interference

REFLECTION

Reflections - the change in direction of a wave when met with a mirror-like obstacle

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Reflections can be observed with light waves, sound waves, and water waves.

  • With light waves, reflection causes the direction of light to change, and thus hit another object

  • With sound waves, reflection causes echoes

    • sound reflection is used in sonar technology

  • If water waves hit a plane, they reflect in the opposite direction

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The law of reflection - the angle of incidence of a wave on a reflective surface is equivalent to the angle of reflection​​​ of that wave (see Fig. 1)

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The law of reflection applies to all sorts of waves, however, the nature of the wave may change the way it interacts with or is affected by reflective surfaces (note that 'reflective surface' here does not mean reflective in the optical sense). For example, light waves bounce entirely off of highly reflective surfaces, but in situations involving sound waves, part of the incident ray will be transmitted to the medium it is in contact with. 

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Incident ray - the first ray/wave to hit the reflective surface or plane

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Reflected ray - the ray that is reflected off the surface or plane

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Normal ray - the ray that is perpendicular to the surface and bisects the incident and reflective rays

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Fig. 1 - Demonstration of the law of reflection.

Waves striking a highly smooth and reflective surface causes specular/regular reflection; waves striking a rough or uneven surface causes a diffuse reflection (see Fig. 2). A diffuse reflection is also produced when waves are incident on convex surfaces.

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Fig. 2 - Diffuse reflection and specular/regular reflection of light waves.

If the reflective surface, rather than being a plane, is parabolic (curved), the incidents waves converge to a single point called the focal point (see Fig. 3).

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Fig. 3 - Convergence of waves to a focal point on a concave surface. 

REFRACTION

Refraction - a change in direction of a wave after passing from one medium to another; the bending of waves as they travel through varying mediums, often accompanied by a change in speed and wavelength

 

The speed of a wave is dependent on the properties of the medium it travels in.

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Refractive index - a dimensionless number that quantifies how light refracts through a medium; a number that indicates the number of times slower that a light wave would be in a given material than it is in a vacuum

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Fig. 4 - Equations that can be used to find the refractive index of light; 'c' is a constant which represents the speed of light in air (3 * 10^8)

Refracted ray - a ray that undergoes a change of velocity (speed, direction, or both) as a result of interaction with a medium

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The close to the normal ray that the refracted ray is, the denser the medium is - in denser mediums, the speed of the refracted ray also decreases. Therefore, a denser medium will generally result in decreased velocity of the refracted ray; the refracted ray will also bend closer towards the normal ray (see Fig. 5).

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Fig. 5 - Diagrams demonstrating refraction in different mediums; the orange ray is the incident ray, the dotted line is the normal ray, and the green ray is the refracted ray in a denser medium than the brown refracted ray

DIFFRACTION

Diffraction - the bending of waves as they pass through openings or around barriers in their paths

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WAVE PROPERTIES

All waves have certain properties that allow us to quantify and classify them.

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Oscillation - one oscillation is equal to one wave, starting from the rest point and hitting the rest point twice more in order to complete one entire wave

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Wave properties:

  • Frequency (f) - the number of oscillations that pass through a point in a second​

    • SI unit is Hertz (Hz)​

  • Wavelength (λ) - the length of one wave; the consecutive distance from one crest to a trough

    • ​SI unit is meters (m)

  • Velocity (v) - the wave's speed (in a specific direction); the product of frequency and wavelength​

    • SI unit is meters per second (m/s)​

  • Time-period (t) - the time it takes for one oscillation to occur​

    • SI unit is seconds (s)​

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LONGITUDINAL & TRANSVERSE WAVES

Waves can be categorized by the direction in which particles of the medium move relative to the direction of the wave (see Fig. 6).

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Transverse waves - waves in which oscillations occur perpendicular to the direction of energy transfer or the propagation of the wave, e.g. water waves, EM waves, seismic waves

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Longitudinal waves - waves in which oscillations occur parallel to the direction of energy transfer or the propagation of the wave, e.g. springs

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Fig. 6 - Transverse & longitudinal wave diagrams.

TRANSVERSE WAVE

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​Properties of a transverse wave:

  • Center line - depicts the wave at an equilibrium wherein no energy is being carried
     

  • Crest - depicts the spot on the wave with the greatest upwards displacement from the equilibrium line
     

  • Trough - depicts the spot on the wave with the greatest downwards displacement from the equilibrium line
     

  • Amplitude - depicts the distance from the equilibrium point to the spot of greatest displacement of the wave from the rest position (the crest and trough). The amplitude can be represented by a vertical extension from the rest point to the crest/trough
     

  • Wavelength - the length that one oscillation covers; the length remains constant throughout a wave, but can be measured from any part of the wave. Most typically, the wavelength is depicted by drawing a line from the wave hitting the rest position twice, after a crest and trough

LONGITUDINAL WAVE

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​Properties of a longitudinal wave:

  • Compression - the area where particles in a medium are closest together
     

  • Rarefaction - the area where particles in a medium are farthest apart
     

  • Wavelength - the length between one rarefaction and another, or the length between one compression and another (as portrayed by the two black circles on the diagram)

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