Physics, Waves and WPD, 5-8

Waves

Progressive Waves

Progressive waves transfer energy without transferring any matter. There is no net movement of the medium, although each particle does oscillate around its equilibrium position.

Transverse Waves

In a transverse wave, particles oscillate at right angles to the direction of propagation.

Longitudinal Waves

In a longitudinal wave, particles oscillate parallel to the direction of propagation. These have compressions and rarefactions.

Mechanical and Electromagnetic Waves

Mechanical waves transfer energy through a medium by the oscillation of particles, and can be transverse or longitudinal.

EM waves are not mechanical, and no not require a medium to propagate.

  • Linked electric and magnetic fields

  • Regions of space when an electric charge would experience a force

  • As an EM wave passes, the electric and magnetic fields oscillate

  • Electric field changes, inducing a magnetic filed perpendicularly

  • Magnetic field varies, changing electric field

  • Wave is self perpetuating

  • EM waves are always transverse

Wave Properties

  • Displacement is measured from the equilibrium position, and can be positive or negative

  • Maximum displacement is equal to the amplitude

  • The amount of energy transferred by a wave is dependent on its amplitude

  • Wavelength sis the distance between two consecutive points with identical displacement and velocity

Phase

  • Two points exactly one wavelength apart are in phase - they oscillate in step with each other

  • Two points half a wavelength apart are in antiphase

  • Phase difference is dependent on the fraction of a wavelength between two points

  • One wavelength is represented by 360°

  • Two points with a phase difference of 360°are in phase

  • Two points with a phase difference of 180°are in antiphase

  • One radian is equivalent to 180°

  • \(360^{\circ}=2\pi\)

Frequency

The time taken for one complete wave to pass a certain point is its period, \(T\). The phase difference can then be described as the fraction of a period between two points.

\begin{gather*} f=\frac{1}{T} \\ T=\frac{1}{f} \\ \end{gather*}

Wave Speed

The speed of a wave depends on the properties of the medium. For a mechanical wave, it depends on:

  • The size of the forces between oscillating particles - the elasticity of the medium

  • The intertia of the vibrating particles - how easy or difficult it is to accelerate each particle

  • Sound travels faster through solids because of the stronger forces between adjacent particles

  • \(v=f\lambda\)

Polarisation

Polarisation is a phenomenon displayed by only transverse waves. If the oscillations are confined to one plane, then the wave is plane polarised. The electric field is always taken to be the plane of polarisation. Light can be polarised using a filter. A polaroid filter absorbs light that is polarised in a plane parallel to the chain molecules.

Light can also be polarised by reflection from a non-metallic surface. Light reflected from the material is polarised parallel to the plane.

Light that is reflected in random directions by a rough surface or small particles is said to be scattered, and is at least partially polarised.

Polarisation of radio waves

The receiving aerial must match the direction of the electric field. Different signals are transmitted in different planes to avoid interference.

Optical Activity

Optically active materials can rotate the plane of polarisation of light, such as sugar solution. Some optically active materials are also affected by stress, which is useful when viewed through a polarising filter.

Superposition of Waves

Principle of Superposition - when two similar waves meet, the total displacement is the vector sum of the two individual displacements. Waves in antiphase will cancel out.

Stationary Waves

Stationary waves are formed by two progressive waves of the same frequency traveliling in opposite directions.

  • Nodes are stationary points, where the two waves are in antiphase.

  • Anti-nodes are points of maximum displacement, where the waves are in phase

  • There is always half a wavelength between two successive nodes or antinodes

  • No energy is transferred along a stationary wave

  • They are formed in systems that have boundaries

  • Progressive waves are reflected and superimposed

  • All points between consecutive nodes are in phase - they all reach their maximum displacement at the same time

Waves on Strings

With certain frequencies, a standing wave can be established on a string. These frequencies are known as harmonics. They depend on:

  • Tension

  • Mass per unit length

  • Length

Also,

  • A fixed point is always a node

  • The lowest frequency is the fundamental frequency, AND the first harmonic

  • \(f_{n}=\frac{nc}{2l}\), with \(n\) being the \(n\)th harmonic

  • \(c=\sqrt{\frac{T}{\mu}}\)

Standing Waves in Pipes

Longitudinal standing waves can be established in a pipe.

  • A closed end is always a node

  • An open end is always an antinode

  • All harmonics exist in an open pipe

  • Only odd harmonics exist in a closed pipe

Applying the Properties of Waves

Stationary EM waves can be established. A laser can be reflected back on itself to direct a stream of atoms very precisely. This is done as the wave deflects atoms, depositing them in a predetermined arrangement.