chapter 6 Flashcards
when does superposition happen?
when two or more waves pass through each other
what does the principle of superposition say?
that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
what is constructive interference?
where two crests meet and two troughs meet. The resultant wave will be twice as big as the original if the first two waves are the same
what is destructive interference?
where a crest and a trough meet of equal size they cancel each other out completely
what happens if the crest and trough aren’t the same size?
then the destructive interference isn’t total. for the interference to be noticeable, the two amplitudes should be nearly equal
what can you use to show superposition and what are they?
phasors which a little rotating arrows to represent the phase of each point on a wave. The phasor rotates anticlockwise through one whole turn as the wave completes a full cycle
what does the length of the arrow show?
the amplitude of the wave
how can you find the resultant at time t?
add the phasors tip to tail.
what does in phase mean?
two points on a wave are in phase if they are both at the same point in the wave cycle
what is one complete cycle of a wave shown as?
as an angle of 360 degrees of 2pi radians
points that have a phase difference of 0 of a multiple of 360 degrees are what?
in phase- their phasors point in the same direction
point with a phase difference of odd-number multiples of 180 degrees or pi radians are what?
exactly out of phase, called antiphase. their phasors point in opposite directions.
when can two different waves be in phase?
because both waves came from the same oscillator
how do you get clear interference patterns?
the two sources must be coherent
what does coherent mean?
two sources are coherent if they have the same wavelength and frequency and a fixed phase difference between them
what does constructive or destructive interference depend on?
path difference- the amount by which the path travelled by one wave is longer than the path travelled by the other wave
when will you get constructive interference? (path difference)
at any point an equal distance from both sources or where the path difference is a whole number of wavelengths. at these points the two waves are in phase and reinforce each other.
when will you get destructive interference? (path difference)
where the path difference is half a wavelength, one and a half wavelengths, 2 and a half wavelengths etc, the waves arrive out of phase
constructive interference occurs when:
path difference= n x wavelength (where n is an integer)
destructive interference occurs when:
path difference= ((2n + 1 ) x wavelength) /2 = (n+0.5)x wavelength
define a standing wave
a standing wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions
unlike progressive waves what isn’t transmitted by a standing wave?
energy
how can yo demonstrate standing waves?
by setting up a driving oscillator at one end of a stretched string with the other end fixed. The wave generated by the oscillator is reflected back and forth.
when won’t the resultant pattern be a jumble?
if the oscillator happens to produce an exact number of waves in the time it takes for a wave to get to the end and back again, then the original and reflected waves reinforce each other
what happens for ‘resonant frequencies’?
you get a standing wave where the pattern doesn’t move
what do standing waves in strings form?
oscillating ‘loops’ separated by nodes
what are nodes?/
each particle vibrates at right angles to the string. Nodes are where the amplitude of the vibration is zero
what are antinodes?
are points of maximum amplitude
at resonant frequencies how many wavelengths fit on the string?
an exact number of half wavelengths
Describe the lowest possible resonant frequency
Called the fundamental frequency. It has one ‘loop’ with a node at each end
What is the second harmonic or first overtone?
It is twice the fundamental frequency. There are two ‘loops’ with a node in the middle and one at each end
What is the third harmonic or second overtone?
Is three times the fundamental frequency. 1 1/2 wavelengths fit on the string
what type of waves are the notes played by string instruments? and how does it work?
transverse standing waves- your finger or the bow sets the string vibrating at the point of contact. Waves are sent out in both directions and reflected back at both ends
what type of waves are the notes played by wind instruments? how does it work in a column of air? in a closed end?
longitudinal standing waves- 1.if a source of sound is placed at the open end of a column of air, there will be some frequencies for which resonance occurs and a standing wave is set up
- if the instrument has a closed end, a node will form there. You get the lowest frequency when the length,l, off the pipe is a quarter wavelength l= wavelength/4
- antinodes form at the open ends of pipes, if both ends are open, you get the lowest resonant frequency when the length,l, of the pipe if a half wavelength l=wavelength/2
how can you demonstrate standing waves with mirowaves?
microwaves reflected off a metal plate set up a standing wave- can find the nodes and antinodes by moving the probe between the transmitter and the reflecting plate
define diffraction
waves spread out as they come through a narrow gap or go round obstacles
when is diffraction unnoticeable?
when the gap is a lot bigger than the wavelength
when do you get noticeable diffraction?
through a gap several wavelengths wide
when do you get most diffraction?
when the gap is the same size as the wavelength
how can you demonstrate diffraction in light?
using laser light through a very narrow slit onto a screen. you can alter the amount of diffraction by changing the width of the slit.
can do the same with white light and a set of colour filters. the size of the slit can be kept constant while the wavelength is varied by putting different colour filters over the slit.
why do you get shadows?
where the wave is blocked, the wider the obstacle compared with the wavelength of the wave, the less diffraction you get and so the longer the shadow
what happens if the wavelength of a light wave is roughly similar to the size of the aperture?
you get a diffraction pattern of light and dark fringes- bright central fringe with alternating dark and bright fringes on either side of it
the narrower the slit,
the wider the diffraction pattern
where is the brightest point of a diffraction pattern?
when light passes in a straight line from the slit to the screen. All the light waves that arrive there are in phase. The phasors all point in the same direction are they hit the screen and add to form a large resultant. Light paths are almost parallel.
what happens are the less bright points where light hits the screen?
there is a constant phase difference between the waves arriving there, so the phasors point in slightly different directions and form a smaller resultant.
what are dark fringes due to?
where the phase difference between the light waves means their phasors add to form a circle, giving a resultant of zero.
how do you demonstrate two- source interference in water and sound?
need coherent sources-( wavelength and freq, have to be the same). use the same oscillator to drive both sources. for water, one vibrator drives two dippers. for sound, on oscillator is connected to two loud speakers.
how do you demonstrate two- source interference for light?
Young’s double-slit experiment:
1) can’t get two separate coherent light sources because light from each source is emitted in random bursts. Instead a single laser is shone through two slits.
2) laser light is coherent and monochromatic
3) the slits have to be about the same size as the wavelength of the laser light so that it is diffracted- then the light from the slits acts like two coherent point sources.
4) you get a pattern of light and dark fringes, depending on whether constructive or destructive interfere
how do you demonstrate two- source interference with microwaves?
replace the laser and slits with two microwave transmitter cones attached to the same signal generator. and replace the screen with a microwave receiver probe. move the probe along a straight path and you’ll get an alternating pattern of strong and weak signals.
what is young’s double-slit formula?
fringe spacing (X)= (distance from screen to slits (L) x wavelength)/ spacing between slits (d)
wavelength= Xd/ L
what does fringe spacing mean?
the distance from the centre of one minimum to the centre of the next minimum or from the centre of one maximum to the centre of the next maximum
why is high ratio of L/d needed to make the fringe spacing big enough to see?
since the wavelength of light is so small
how do you get a more accurate value of fringe spacing (X)?
measure across several fringes then divide by the number of fringe widths between them
what were the two theories of light published in the 17th century?
Newton’s theory suggest light was made up of tiny particles called “corpuscles”-could explain relfection and refrction but not diffraction and interference (wave properties). and Huygens put forward a theory using waves
when do interference patterns get sharper?why?
when you diffract through more slits because there are so many beams reinforcing the pattern
what do sharper fringes make to measurements?
more accurate
for monochromatic light, all maxima are
sharp lines
what is the line of maximum brightness at the centre called?
the zero order line
what are lines either side of the zero order line called?
first order lines-> 2nd order lines etc
what is the nth order maximum given by?
d sin angle = n x wavelength
d= distance between slits angle= angle between the incident beam n= number of order maximum
if the grating has N slits per metre then the slit spacing, d, is?
1/N metres
if the wavelength is bigger, sin angle will be bigger so the angle will be bigger, what does this mean?
that the larger the wavelength, the more the pattern will spread out
if d is bigger, sin angle is smaller, what does this mean?
that the coarser the grating, the less the pattern will spread out
how do you know that an order doesn’t exist?
when values of sin angle are > 1 because that’s impossible
what happens if you diffract white light through a grating?
then the patterns due to different wavelengths within the white light are spread out by different amounts
with white light what happens to each order?
it becomes a spectrum, with red on the outside and violet on the inside. The zero order maximum stays white because all the wavelengths just pass straight through
why do astronomers and chemists use diffraction gratings rather than prisms?
they often need to study spectra to help identify elements, diffraction grating are more accurate than prisms.
