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Diffraction of Water Waves
Diffraction of Water Waves
- Diffraction - the spreading of waves around corners.
- waves reflect off of barriers
- If there is a small opening, or the wave can move past a sharp edge, then the wave bends or changes direction.
- The amount of diffraction is determined by the size of opening and wavelength
- The greater the ratio l/w (w is the opening width), the more diffraction.
- For the diffraction to be a maximum, l/w is greater than or equal to 1.
- Sound moves around corners due to diffraction.
- Low sounds diffract more than high sounds.
- If two identical sources produce waves then
- the frequency for both are the same
- wavelength for both are the same
- amplitude for both are the same
- both are in phase
- The waves will pass through each other unchanged
- Sometimes
- crest will meet crest to produce constructive interference.
- trough will meet trough to produce constructive interference.
- crest will meet trough to produce destructive interference.
- Various areas of constructive and destructive interference are produced.
Interference of Waves in Two Dimensions
Interference of Waves in Two Dimensions
- Antinodal lines – lines joining points of maximum constructive interference.
- Nodal lines – lines joining points of maximum destructive interference.
- Nodal points – points where a crest meets a trough.
- there is constant zero displacement of the medium.
- there is destructive interference.
- Antinodal point – points where a crest meets a crest or a trough meets a trough.
- There is oxcillation between maximum positive and maximum negative displacement.
- there is constructive interference.
- The crests and troughs move outwards from the sources but the entire pattern of nodal and antinodal lines remains constant.
- The pattern of nodal and antinodal lines changes if
- frequency of the source changes (if frequency increases, the distance between lines decreases).
- phase of one of the sources changes (the pattern shifts right or left).
- distance between sources change (if the distance between sources increases, the number of lines increases).
Mathematical Analysis of the Two Point Source Interference Pattern
Mathematical Analysis of the Two Point Source Interference Pattern
- Observing an interference pattern allows us to determine the wavelength.
- In general for antinodal lines
- For nodal lines we can similarly determine that
- Central antinodal line – The antinodal line in the center of the pattern
- The other lines are numbered with respect to the central antinodal line.
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