1.2 WavesWavesWave on a stringSlide 4Transverse and Longitudinal WavesExamples of wavesSlide 7Slide 8Slide 9ExampleTransverse wave on a stringSpeed of the transverse wave on a string.Slide 13Superposition PrincipleInterferenceConstructive InterferenceDestructive InterferenceOther Interference EffectsReflection and Transmission.Mis-match at the boundaryReflection1.2 Waves• Wave properties– speed– wavelength• Example wave on a string• Superposition of waves• Reflection of waves at an interfaceWaves•A wave is a disturbance that propagates through distance with a certain speed. The disturbance carries energy but does not carry mass. (called traveling waves)•Mechanical Waves- water wave, sound – propagate through matter.•Electromagnetic Waves – radio, x-ray, light – can propagate through a vacuum.Wave on a stringincreasing timeTransverse Wave - The displacement is perpendicular to the direction of propagationLongitudinal Wave- The displacement is parallel to the direction of propagationTransverse and Longitudinal WavesTransverse and Longitudinal Waves•The transverse and longitudinal waves depend on different mechanical properties of the material.•Two polarizations of transverse waves. Longitudinal waves are unpolarized.•The speed of the transverse and longitudinal waves are different.Examples of waves•Transverse waves–Transverse wave on a string– Electromagnetic waves (speed = 3.00x108 m/s)•Longitudinal waves–Sound waves in air (speed = 340 m/s)Simple Harmonic WavesPeriodic displacement vs distanceHarmonic oscillationsWavelength - Spatial PeriodWave travels distance  during one period TWave velocityv fTl= =lExampleA radio station transmits at a frequency of 100 MHz. Find the wavelength of the electromagnetic waves. (speed of light =3.0x108 m/s)v f=lvfl =863.0x103.0m100x10= =Transverse wave on a stringv ->uv is the wave speedu is the speed of the string perpendicular to direction of v.The mass at P undergoes simple harmonic motion.Speed of the transverse wave on a string.FFV ->xDmDmxDm=Dmass densityFv =mspeed of transverse wave on a string depends on the tension onthe string and the mass densityExample A transverse wave with a speed of 50 m/s is to be produced on a stretched spring. If the string has a length of 5.0 m and a mass of 0.060 kg, what tension on the string is required.Fvm /L=2v mFL=2(50m / s) (0.060kg)30N5.0m= =Superposition Principle•When two waves overlap in space the displacement of the wave is the sum of the individual displacements.Interference•Superposition of harmonic waves depends on the relative phase of the two waves•Can lead to–Constructive Interference–Destructive InterferenceConstructive Interferencedistance Wave 1Wave 2SuperpositionThe two waves have the same phaseDestructive InterferenceWave 1Wave 2SuperpositionThe two waves are out of phase (by 180o , i.e. )Other Interference Effects Many other effects arise from superposition of harmonic waves – discussed later.Standing waves. two waves traveling in opposite directions.Beats. two waves with different frequencies.Diffraction. Interference in wave patterns in space.Reflection and Transmission.•When a wave reaches a boundary, part of the wave is reflected and part of the wave is transmitted. •The amount reflected and transmitted depends on how well the media is matched at the boundary.•The sign of the reflected wave depends on the “resistance” at the boundary.Mis-match at the boundaryBoundarymatchmis-matchmis-matchPart of the wave will be reflected at the boundaryReflectionFixed End- InversionFree End- No Inversionstrong