Waves

Waves

Waves and vibrations

Mechanical waves

• -Waves that pass through substances are vibrations which pass through that substance

• -Waves that pass through a substance are mechanical waves

• -Examples include seismic waves, sound waves and waves on strings

• -When these waves pass through substances the particles of the substance vibrate which causes other particles to vibrate in the same way

Electromagnetic waves

• Are oscillating electric and magnetic fields

• Don’t need a medium to be transmitted

• Vibrating electric field generates magnetic field which generates electric field etc.

• Examples include the EM spectrum

Longitudinal and transverse

• Longitudinal: Waves where direction of vibration is parallel to direction of wave travel

• Transverse: waves which direction of vibration is perpendicular to direction of travel

• Primary seismic waves are longitudinal but secondary are transverse

Polarisation

• Transverse waves plane polarised if vibrations are only in one plane

• Longitudinal waves cannot be polarised

• Light from filament lamp or candle unpolarised – if passed through filter then light is polarised

• If unpolarised light passed through 2 polaroid filters, then light intensity changes depending on how one filter is turned relative to the other

• Then one filter perpendicular to other no light can pass through as light not travelling in the same plane

• Plane polarisation of an EM wave defined as plane where electric field vibrates

Measuring waves

Key terms

• The displacement of a vibrating particle is its distance and direction from its equilibrium position

• Amplitude of a wave is the max displacement of a vibrating particle

• Wavelength (λ) least distance between two adjacent vibrating particles with same displacement and velocity at same time

• One complete cycle of a wave is from max displacement to next

• Period of a wave is time for one complete wave to pass a fixed point

• Frequency is number of cycles per second (or number of complete waves passing a fixed point per second)

Wave speed

• Higher frequency of a wave, the shorter its λ
• Speed of waves (c) = frequency (f) × wavelength (λ)

Phase difference

• Phase of a vibrating particle at a certain time is the fraction of a cycle it has completed since the cycle started

• Phase difference between two particles is fraction of cycle between the particles

• Measured in radians - 2π radians in one λ

Wave properties

Ripple tanks

• Used to observe properties such as reflection, refraction and diffraction

• Waves observed in ripple tank called wavefronts (lines of constant phase eg. crests)

• Direction in which wave travels is perpendicular to the wavefront

Reflection

• Straight waves directed at a hard flat surface reflect off at the same angle as they were directed at (angle of incidence = angle of reflection)

• Angle between incident ray and plane mirror is equal to the angle between the reflected ray and the mirror

Refraction

• When waves pass across a boundary to material of different density the speed changes so λ changes (freq stays constant)

• If wavefronts approach at an angle, then they change direction – this is refraction

Diffraction

• Occurs when waves spread out after passing through a gap or around an obstacle

• The narrower the gap the more the waves spread out

• The longer the wavelength the more the waves spread out

More wave properties

Superposition

• When waves meet they pass through each other

• At the point where they meet they combine for an instant before they more apart (superposition)

• Principle of superposition states that when two waves meet, total displacement at a point is equal to the sum of the individual displacements at that point

• When 2 crests meet supercrest created (reinforcement) – same for two troughs

• When a crest and a trough of same amplitude meet, they cancel out (resultant displacement of 0)

• Interference is where waves of constant freq and constant phase difference cancel and reinforce at fixed points

• Coherent sources of waves produce interference pattern where they overlap as same freq waves with constant phase difference

• If phase difference randomly changed, points of cancellation and reinforcement would change at random and no interference pattern seen

Stationary and progressive waves

Formation of stationary waves

• Stationary wave formed when two progressive waves pass through each other if they have same freq and constant phase difference

• Fundamental mode of vibration: simplest stationary wave – contains 2 nodes (zero displacement) and one antinode (max displacement)

• Distance between adjacent nodes if half a wavelength

• Stationary waves that vibrate freely don’t transfer energy to their surroundings

• No vibrations at nodes (no energy) and max at antinodes (max energy) so as nodes and antinodes at fixed positions, no energy transferred

Stationary waves explanation

• Phase difference between two vibrating particles is: 0 if the two particles are between adjacent nodes or separated by even number of nodes, Π radians is two particles separated by odd number of nodes

Stationary waves vs progressive waves

Frequency

Stationary - all particles except nodes vibrate at same freq

Progressive - all particles vibrate at same freq

Amplitude

Stationary - amplitude varies from 0 at nodes to max at antinodes

Progressive - amplitude same for all particles

Phase difference

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