Superposition and interference (to be continued

what is the principle of superposition

when two waves meet at a point the resultant displacement at that point is equal to the sum of the displacements of the individual waves

how do noise cancelling headphones work

• a microphone on the outside of the headphones detects the background noise

• the speakers inside the headphones produce waves that aim to perfectly cancel out all external sounds through destructive interference

what is interference

when two progressive waves continuously pass through each other they superpose and produce a resultant wave with a displacement equal to the sum of the two individual displacements

constructive interference

• if the two waves are in phase then the maximum positive displacements from each wave line up and create a resultant displacement with increased amplitude

• as intensity is proportional to amplitude squared, the increase in amplitude causes an increase in intensity, so the sound waves are louder and light is brighter

destructive interference

• if two progressive waves are in antiphase, the maximum positive displacement of one wave lines up with the maximum negative displacement from the other, and the resultant displacement is smaller

• if the two waves have the same amplitude then the resultant wave will have 0 amplitude so will be completely cancelled out

interference pattern

• the pattern in which at different points the superposed waves are in phase or out of phase, creating a repeating pattern of constructive and destructive interference (if the waves are coherent)

coherence

when waves emitted from two sources have a constant phase difference and the same frequency (so they have a stable and periodic interference pattern)

path length

the distance the wave travels, measured in multiples of the wavelength

path difference

• the differences between the distances that two waves travel

• alternative definition: the fraction of a wavelength by which two points’ oscillations are separated
  

maximum

where the waves interfere constructively and are in phase, so the displacement increases (at this point the path difference is 0 or a whole number of wavelengths and the phase difference is 0 or an even multiple of pi)

minimum

where the waves interfere destructively and are in antiphase, so the amplitude decreases and appears to be 0 (at this point the path difference is an odd number of half wavelengths and the phase difference is 180 or pi)

sound waves superposition

•two audio signal generators emit coherent waves which overlap and form an interference pattern

•when a microphone connected to an oscilloscope is moved parallel to the speakers, regions of loud and quiet will be seen

Young's double slit experiment

•a laser that produces monochromatic light is placed behind a sheet with two slits in it

•the two coherent waves overlap and superpose, creating alternating bright and dark fringes

•the equation wavelength=ax/d can be used to find the wavelength

what is a diffraction grating (we didn't really cover it in class but still)

•its a piece of transparent material with many opaque lines scratchedin it

•the light passes through the transparent slits and produces an interference pattern with maxima and minima

•dsin theta= n × wavelength where d is slit spacing, theta is angle between 0 and nth maxima, n is order of maxima, wavelength is wavelength