Topic 4 – Oscillations and Waves4.4 Wave Properties
Reflection and Transmission● When a wave crosses a boundary between 2media the wave will be partly reflected andpartly transmitted.● The amount of reflection and transmissiondepends on the nature of the boundary.● If the wave is able to move at the boundary then thereflected wave will be in phase. (A Soft Boundary)● If the wave is fixed at the boundary then thereflected wave will be out of phase. (A HardBoundary)
Reflection and Transmission● As waves move from onemedium into another the waveis partially transmitted andpartially reflected.● If the boundary is from lowdensity to high density thenthis is a hard boundary andthe reflected wave suffers aphase change.● If the boundary is from highdensity to low density thenthis is a soft boundary and thereflected wave is reflected inphase.θiθRθr
The Law of Reflection● The angle of incidence always equals the angleof reflection.θiθR
Changing Media● As waves move from one medium into another theirwavespeed will change.● Transverse waves usually have more resistance topropagation in dense materials● The wave will therefore usually travel slower in moredense materials.● The refractive index (1n2) is the ratio of the speeds tothe wave in medium 2 to that in medium 1● The absolute refractive (n2) index is that when medium1 is a vacuum, i.e. cn2.
Refractive Indices● The refractive indices of some commonmaterials are shown below.● Calculate the speed of light in these materialsMaterial n v x108ms-1Air 1.0003Water 1.333Perspex 1.49Crown Glass 1.52Diamond 2.42
Changing Media● When a wave crosses a boundary between twomedia at an angle other than the normal it willchange direction.● This is called refraction● The amount of refraction is predicted by Snell’slaw: sin θisinθr=vivr=nrni
Refraction● When light crosses from aless optically densemedium into an moreoptically dense mediumthe light refracts towardsthe normal.● When light crosses from amore optically densemedium into an lessoptically dense mediumthe light refracts away thenormal.θiθr
Refraction and Critical Angle● The use of a semi-circular block of mediumallows the effect of moving from a highoptical density to a low optical density to bestudied.● Any ray that enters the block along a radiuswill strike the curved surface normally andhence will not refract.● As light exits a material into air or thevacuum it will refract away from the normal.● At some angle of incidence, the refractedray will be directly along the flat surface ofthe block.● This is known as the critical angle θc.● The refractive index of the medium canhence be determined.θcsinθisinθr=nrnini=nr sinθrsinθin=1sin 90sinθcn=1sinθc
Diffraction● When a plane waveencounters a gap in abarrier then the waves thatpass through will becomecurved at the edges andspread out.● This is called diffraction.● This is the phenomenonthat allows sound to“travel around corners”● The amount of diffractiondepends on the ratio of thewidth of the gap and thewavelength.
Diffraction● If the gap width (d) ismuch larger than thewavelength then thewave passes throughwith only smalldiffraction.
Diffraction● If the gap width (d) islarger than thewavelength then thewave passes throughwith only morediffraction.● The wave ends startto noticeable curve
Diffraction● If the gap width (d) isslightly wider than thewavelength then thewave passes throughwith a lot ofdiffraction.● The wave looks morecurved than straight
Diffraction● If the gap width (d) isexactly the samewidth as thewavelength then thewave passes throughand forms perfectlycircular waves.● There are now noshadows
Examples of Diffraction● Water waves areoften seen diffractingas they enter aharbour.● Sound can be heardaround a corner dueto diffraction
Examples of Diffraction● Light also diffracts but thisis much less noticeablethan sound because of theshort wavelength of light.● Often the image sufferschromatic aberration● Different colours of lighthave differentwavelengths so arediffracted by differentamounts.● This colour splitting isknown as dispersion
Superposition● Two waves that exist in thesame space are able topropagate through eachother.● When the two wavesinteract, the resultant waveform is that formed by thesuperposition of the twowaves.● Superposition is the vectoraddition of the twoamplitudes.
Superposition● If the two waves are inphase at the interaction,then the amplitudeincreases.● This is constructivesuperposition.● If the two waves are outof phase at theinteraction, then theamplitude is zero.● This is destructivesuperposition.
Superposition and Harmonics● Musical Instrumentsrarely produce purenotes.● Usually additionalharmonics areaudiable.● If the fundamentalfrequency of a stringinstrument is f, thenthe harmonics are:● 2f, 3f, 4f etc.