Today 1/17 Interference HW: 1/17 HW Handout “Interference”

Due Thur, 1/23 (beginning of class) Today’s goal:

Predict locations where constructive and destructive interference occur.

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

In this case the sources are in “sync” and produce waves of equal wavelength. The wave velocity depends only on the medium and so is the same for both.

Where are the locations of constructive and destructive interference?

c c cd d

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

How would your answer change if the sources were out of sync?

midpoint

This picture now includes the sources of the waves.

Source 1 Source 2

Out of sync means that one produces a crest while the other produces a trough--it’s a timing thing.

c cd d

How would your answer change if the sources were out of sync?Now the locations for constructive and destructive interference switch!

d

c c cd dSources in phase (in sync)

Sources out of phase (out of sync)

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

In any case, the interference occurs in a pattern. The next job is to invent a rule so we can predict these locations.

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

What do you need to predict interference?

1. Whether the sources are in phase or not

2. Wavelength

3. Location

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

We want one thing we can say about all these places for “in phase and constructive.”

The difference in distance from each source to constructive locations is given by...

PL2 - PL1 = Path Length Difference = PLD = n, n = 0,1,2,3...

PLD = 0PL1 PL2

2 2

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

Now what can we can say about the places for “in phase and destructive.”

The difference in distance from each source to destructive locations is given by...

Path Length Difference = PLD = (n + 1/2), n = 0,1,2,3...

1/23/2 1/2 3/2

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

What about the places for “out of phase and constructive.”

The difference in distance from each source to constructive locations is...

Path Length Difference = PLD = (n + 1/2) , n = 0,1,2,3...

1/23/2 1/2 3/2

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

What about the places for “out of phase and destructive.”

The difference in distance from each source to destructive locations is...

Path Length Difference = PLD = n, n = 0,1,2,3...

PLD = 0

2 20

Source 1 Source 2c cd d d

Sources out of phase (out of sync)

c c cd dSources in phase (in sync)

Source 1 Source 2

PLD = (n + 1/2), n = 0,1,2,3...

PLD = 0

Summary:

In phase, constructiveIn phase, destructiveOut of phase, constructiveOut of phase, destructive

PLD = (n + 1/2), n = 0,1,2,3... PLD = n, n = 0,1,2,3...

PLD = n, n = 0,1,2,3...

Interference in 2-DSources “in phase”

Crest meets crest and trough meets trough, constructive, loud sound or bright light

Crest meets trough and trough meets crest, destructive, no sound or dark

Crest

Trough

Interference in 2-DSources “in phase”

Constructive at a point if it is the same distance from each source

Destructive at a point if it is 1/2 farther away from one source

Crest

Trough

Interference in 2DSources “out of phase”

Crest meets trough and trough meets crest, destructive, no sound or dark

Crest meets crest and trough meets trough, constructive, loud sound or bright

Crest

Trough

Interference in 2-DSources “out of phase”

Destructive at a point if the point is the same distance from each source

Constructive at a point if the point is 1/2 farther away from one source

Crest

Trough