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Two Point Source Interference Pattern - PowerPoint PPT Presentation

Two Point Source Interference Pattern. A Mathematical Analysis. 2 Point Interference Pattern. Nodal Lines. Nodes are areas of destructive interference and antinodes are the opposite (constructive) In standing waves, nodes are the particles that appear to stand still

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Two Point Source Interference Pattern

A Mathematical Analysis

• Nodes are areas of destructive interference and antinodes are the opposite (constructive)

• In standing waves, nodes are the particles that appear to stand still

• Nodal lines occur in areas of destructive interference (crest+trough or trough+crest)

• Nodal lines in light interference would be dark

• An antinodal line appears in the centre of an interference pattern when the two frequencies of the sources match)

• The “count” of the nodal and antinodal lines increases as one moves away from the centre antinodal line

PD = | S1A - S2A | = | 5 - 6 | = 1

Point B, on antinodal line 1

PD = | S1B - S2B | = | 3 - 4 | = 1

Point C, on antinodal line 2

PD = | S1C - S2C | = | 4 - 6 | = 2

• Look only at nodal lines

• Remember that nodal line numbers get larger as you move out from centre

• The first nodal line is just to the right of the right bisector of the line joining the sources

• Instead of A,B,C, etc., we will call the general point, P, and use a subscript to denote the nodal line on which it sits

PD = | P1S1 – P1S2 | = | 5–4.5 | = 0.5

PD = | P2S1– P2S2| = | 3.5–5 | = 1.5

Red: Antinodal Lines

• Note that this is only for nodal lines (destructive interference)

• Antinodal lines would have (n-1) instead

PD = | PnS1 – PnS2 | =(n-0.5)l

• Where q is the angle for the nth nodal line from the main nodal line (right bisector)

• l is the wavelength

• d is the source spacing

• qn cannot be larger than 1, the RHS cannot be larger than 1

• The largest n that satifies this condition will be seen in the interference pattern – count them!

• By measuring d and counting nodal lines, we can approximate l

What angle does q measure?

using the diagram to the right.

• Two point sources generate identical waves that interfere in a ripple tank. The sources are located 5.0 cm apart, and the frequency of the waves is 8.0 Hz. A point on the first nodal line is located 10 cm from one source and 11 cm from the other.

• What is the wavelength of the waves?

• [2.0 cm/s]

• What is the speed of the waves?

• [16 cm/s]

• A ripple tank experiment has given the following data from 2 point sources operating in phase: n=3, x3=35cm, L=77, d=6.0cm, q3=25°, 5 crests=4.2cm. Using 3 methods, determine the wavelength of the waves.