The principle of superposition The resultant displacement at any point is the sum of the separate displacements due to the two waves Eg: with a slinky coil spring

The principle of superposition The resultant displacement at any point is the sum of the separate displacements due to the two waves Eg: with a slinky coil spring

supercrest The principle of superposition The resultant displacement at any point is the sum of the separate displacements due to the two waves Eg: with a slinky coil spring

supercrest The principle of superposition The resultant displacement at any point is the sum of the separate displacements due to the two waves Eg: with a slinky coil spring

Two square waves superposing:

Superposition of sine waves:

A square wave can be made up from several sine waves of higher frequencies

Phase changes on reflection LONGITUDINAL PULSETRANSVERSE PULSE

Phase changes on reflection LONGITUDINAL PULSETRANSVERSE PULSE

Phase changes on reflection LONGITUDINAL PULSETRANSVERSE PULSE

Phase changes on reflection LONGITUDINAL PULSETRANSVERSE PULSE

Interference effects Two dippers in a ripple tank can cause circular wavefronts to re-inforce or cancel: Re-inforcement (constructive interference) Cancellation (destructive interference)

Interference effects Two dippers in a ripple tank can cause circular wavefronts to re-inforce or cancel: Re-inforcement (constructive interference) Cancellation (destructive interference) Coherent sources (of the same frequency and phase relationship) produce a stable interference pattern.

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. x x Signal strength

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. x x Signal strength

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) x x Signal strength

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference Regions of reinforcement

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference Regions of reinforcement

Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference Regions of reinforcement Regions of cancellation

compressions rarefaction Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers

compressions rarefaction Regions of reinforcement (LOUD) Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers

compressions rarefaction Regions of reinforcement (LOUD) Regions of cancellation (QUIET) Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers When compressions (or rarefactions) arrive in phase from both speakers, constructive interference occurs, creating a loud region