InterferencePatternsV1p1

Two-Point Source
Interference Patterns

Version 1.1

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Nodes Analyzed:

first order antinodal

AN,AN,AN,AN,AN,AN,AN,AN,AN,AN,AN,AN,AN,AN,N,N,N,N,N,N,N,N,N,N,N,N

0,0,1,1,1,1,2,2,2,2,3,3,3,3,1,1,1,1,2,2,2,2,3,3,3,3

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9,6,9,4,8,5,8.5,6,9.5,4,12.5,9,7,3.5,8.5,5,7,3.5,9,7,7,2.5,8,5.5,6.5,5

9,6,8,3,9,6,6.5,4,11.5,6,9.5,6,10,6.5,8,4.5,7.5,4,7.5,5.5,8.5,4,5.5,3,9,7.5

Can you discover the relationship between the path difference, the wavelength, and the line that the point is on?

Collect data for four points on nodal lines and four points on antinodal lines.

Distance from S2 to

Distance from S1 to

Analyze data for points on four antinodal lines and four nodal lines.

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Antinodes Analyzed:

Path Difference =

Take a Quiz

Change the wavelength and the distance separating the sources and observe the effect that the changes have upon the pattern.

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Analyze several antinodes and nodes to see if you can discover the relationship between the path difference and the wavelength for antinodes and for nodes.

Two-Point Source Interference Patterns

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So you’re just getting acquainted with two-point source interference patterns. We understand. Let us help you with a short tutorial.

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Do It Yourself Patterns

Tutorial on Two-Point Source Interference

Path Difference

Progress

Imagine a shallow tank of water. If the water is disturbed at a single point, ripples spread out across the water’s surface in all directions. Circular waves are produced.

We often represent these circular waves by alternating bold and dashed lines … concentric about the source. Bold lines are crests. Dashed lines are troughs.

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Ripples in a Tank

Change Wavelength:

DIY Patterns

Increase or decrease the wavelength and source separation distance. Observe the effect that such changes have upon the features of the patern.

DrawThis

Change Sep’n Distance:

Do Concept Checker

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PtB

PtA

PtF

PtH

PtI

PtE

PtC

PtD

PtG

0,0,0,0,0,0,0,0

0,0

Start

Version 1.1

These waves will undego constructive and destructive interference.

Wave Interference

In the diagram, the red dots are a few locations where constructive interference occurs. The grey dots are some locations of destructive interference.

Now suppose the water in the ripple tank is disturbed at two locations. There will be two sets of circular waves traveling through the tank.

Antinodes are observed at all the red-dot locations. The water vibrates wildly from a large positive (upward) displacement to a large negative (downward) displacement.

Nodes and Antinodes

Nodes would be observed at the grey-dot locations. The water would be undisturbed (perfectly still) at these locations.

The red dots are locations where crests interfere with crests or troughs with troughs. The grey dots are locations where crests interfere with troughs.

Nodal and Antinodal Lines

The nodes and antinodes lie along lines. These lines are referred to as nodal lines and antinodal lines.

The nodal lines and antinodal lines are given names like … central antinodal line first antinodal line second antinodal line first nodal line second nodal line

What’s in a Name?

These patterns of nodes and antinodes lying along lines and resulting from vibrations of two sources are referred to as two-point source interference patterns.

There are two sources of waves … … located at points. The waves undergo interference to produce a pattern of nodes and antinodes lying along lines.

Nodes would be observed a the grey-dot locations. The water would be undisturbed (perfectly still) at these locations.

Wavelength (λ)

There are some terms you will need to know … like wavelength.

Wavelength is the length of the wave. It is the distance measured from one crest to the next adjacent crest in the radial direction from the source.

You need to be able to “measure” wavelength.

Source Separation Distance (d)

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The source separation distance is the distance between the two sources of waves. The symbol is d. The sources are S1 and S2.

Changing the value of d changes the look of the resulting pattern.

The path difference is often measured in terms of the wavelength (λ). For this example, the path difference is ... | 6•λ - 7•λ | = 1•λ

At the antinode, waves from S1 and S2 meet to constructively interfere. The waves travel along different paths of a different distance to the antinodal point (P)

The path difference (PD) is the difference in distance traveled. PD = | S1P - S2P |

Using R as point P: S1P = 5•λ, S2P = 4•λ, and … PD = | 5•λ - 4•λ | = 1•λ

Using Q as point P: S1P = 4.5•λ, S2P = 6•λ, and … PD = | 4.5•λ - 6•λ | = 1.5•λ

Two More Path Difference Examples

Understanding path difference will be a big part of this activity. Determine S1P and S2P and the path difference for point Q and point R.

Learn More ...

Check out our YouTube channel for additional help with understanding interference patterns. @PhysicsclassroomVideos

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