Waves 2 Flashcards
State the principle of superposition
When two waves meet at a point, the resultant displacement at that point is equal to the vector sum of their individual displacements.
In waves, what is interference?
The superposition of coherent waves to produce a resultant displacement.
What is the phase difference between adjacent antinodes on a stationary wave?
pi radians
Compare progressive and stationary waves in terms of phase difference:
Progressive wave phase changes across one complete cycle, stationary wave all parts of wave between a pair of nodes are in phase
What did the Young double slit experiment give evidence for?
The wave nature of light (because interference patterns are formed)
What is the separation between adjacent nodes on a stationary wave?
lambda/2
How are stationary waves formed?
By two progressive waves of the same frequency travelling in opposite directions (eg by reflection of waves) superposing to form nodes and antinodes
For two coherent in-phase wave sources, under what circumstances is a minimum observed at a point?
When the path difference is (n+1/2)lambda, an odd number of half wavelengths, then destructive interference occurs.
What is destructive interference?
When two waves are in antiphase, the resultant displacement from the superposition of the two waves has a minimum amplitude.
For two coherent in-phase wave sources, under what circumstances is a maximum observed at a point?
When the path difference is nlambda, a whole number multiple of the wavelength, then constructive interference occurs.
Define path difference:
The difference in distance travelled to a specific point by two waves from different sources
Compare progressive waves and stationary waves in terms of energy transfer:
Progressive waves transfer energy, in stationary waves, there is no net transfer of energy
Define coherence
Two coherent waves have a constant phase difference (must be waves of the same type with the same frequency)
If two points on a wave (or two waves) are completely in phase what is their phase difference in degrees and in radians?
Zero (or 360degrees or 2pi radians)
Define phase difference
The difference in phase between two points on the same wave or between two waves (measured in degrees or radians)
Compare progressive waves and stationary waves in terms of wavelength
Progressive waves λ is a minimum distance between two adjacent points oscillating in phase, stationary wave λ is twice distance between adjacent nodes (or antinodes)
Compare progressive waves and stationary waves in terms of ampitude:
Progressive wave all parts of the wave have the same amplitude (if no energy loss)
Stationary wave- maximum amplitude at antinodes dropping to zero at node
If two points on a wave (or two waves) are in antiphase, what is their phase difference in degrees and in radians?
pi radians, 180 degrees
Give the frequency as a multiple of the fundamental and wavelength in terms of length of string for the first five possible harmonics of a stationary wave on a string:
1st harmonic frequency = wavelength = 2L
2nd harmonic frequency = L
3rd harmonic frequency = 2L/3
4th harmonic frequency = L/2
5th harmonic frequency = 2L/5
Give the quantities and their units for the equation λ = ax/D
λ = wavelength (m)
a = slit separation (m)
x = fringe spacing (m)
D = distance from the slits (m)
Give the wavelength in terms of length of tube for the first five possible harmonics of a stationary in an air column closed at one end:
1st harmonic wavelength = 4L
2nd harmonic wavelength = 4L/3
3rd harmonic wavelength = 4L/5
4th harmonic wavelength = 4L/7
5th harmonic wavelength = 4L/9
For air columns in tubes, what must be true for stationary waves at closed and open ends?
Closed end = node (minimum amplitude)
Open end = antinode (maximum amplitude)
Describe nodes and antinodes in terms of phase difference:
At nodes waves are in antiphase so undergo destructive interference.
At antinodes, waves are in phase so undergo constructive interference.
What is constructive interference?
When two waves are in phase the resultant displacement from the superposition of the two waves has a maximum amplitude
Under what circumstances can the equation λ = ax/D be used?
Two sources of monochromatic coherent waves, D»a
(Young double-slit)
Give the wavelength in terms of length of tube for the first fives possible harmonics of a stationary wave in an air column open at both ends:
1st harmonic wavelength = 2L
2nd harmonic wavelength = L
3rd harmonic wavelength = 2L/3
4th harmonic wavelength = L/2
5th harmonic wavelength = 2L/5
