Wave Interference

Behaviour of Waves

Define interference.

The superposition of two or more waves to produce a resultant wave.

What is an interference pattern?

A pattern produced by the superposition of waves, consisting of regions of constructive and destructive interference.

What conditions are needed to produce a stable interference pattern?

The waves must be coherent.

Define coherent waves.

Waves that have the same frequency and a constant phase difference.

What is meant by two-source interference?

Interference produced when waves from two coherent sources overlap.

What happens when two coherent waves meet?

They superpose, producing regions of constructive and destructive interference.

Define constructive interference.

When waves meet in phase and their displacements add to produce a larger resultant amplitude.

Define destructive interference.

When waves meet out of phase and their displacements oppose each other, producing a smaller or zero resultant amplitude.

What is complete destructive interference?

When two waves of equal amplitude meet in antiphase and completely cancel, giving zero resultant amplitude.

What is the phase difference between two waves that are exactly in phase?

0 rad or a whole multiple of 2π rad.

What is the phase difference between two waves that are in antiphase?

π rad or 180°.

What is produced at a point of constructive interference?

A maximum-amplitude region or antinode.

What is produced at a point of complete destructive interference?

A zero-amplitude region or node.

Why can two loudspeakers produce an interference pattern?

If connected to the same signal generator, they produce coherent sound waves that superpose.

Why should two loudspeakers be connected to the same signal generator in an interference experiment?

To ensure they produce waves of the same frequency with a constant phase relationship.

What would you hear at a position of constructive interference between two sound waves?

A loud sound due to the larger resultant amplitude.

What would you hear at a position of destructive interference between two equal sound waves?

A minimum in sound intensity, potentially silence.

What determines the positions of nodes and antinodes in a two-source interference pattern?

The wavelength, separation of the sources and distance from the sources.

What is Young's double-slit experiment?

An experiment in which light from two coherent sources interferes to produce alternating bright and dark fringes.

What did Young's double-slit experiment provide evidence for?

The wave nature of light.

What is observed on the screen in Young's double-slit experiment?

Alternating bright and dark interference fringes.

What causes a bright fringe in a double-slit experiment?

Constructive interference between waves arriving in phase.

What causes a dark fringe in a double-slit experiment?

Destructive interference between waves arriving in antiphase.

What is another name for the bright and dark regions in a light interference pattern?

Fringes.

Why are two slits used in Young's experiment?

The slits diffract the incident wave and act as two coherent sources.

Why must the two sources in Young's experiment be coherent?

A constant phase relationship is required to produce a stable interference pattern.

How can two coherent light sources be produced experimentally?

Illuminate two nearby slits using the same monochromatic light source, such as a laser.

How can two-source interference be demonstrated using water waves?

Use a ripple tank with waves generated through two gaps so that the two wave sources overlap and interfere.

How can two-source interference be demonstrated using sound?

Connect two loudspeakers to the same signal generator and observe variations in sound intensity at different positions.

How can two-source interference be demonstrated using light?

Shine a laser through a double slit and observe the bright and dark fringes on a screen.

Define path difference.

The difference between the distances travelled by two waves from their sources to a particular point.

What determines the phase difference between waves arriving at a point?

Their path difference compared with their wavelength.

Why does path difference produce a phase difference?

A difference in distance travelled means the waves have completed different fractions of a wavelength when they arrive.

How much phase change corresponds to one complete wavelength?

2π rad or 360°.

What path difference corresponds to waves arriving exactly in phase?

A whole number of wavelengths, nλ.

What is the condition for constructive interference in terms of path difference?

Path difference = nλ, where n = 0, 1, 2, 3, ...

What is the condition for constructive interference in terms of phase difference?

Phase difference = 2nπ rad.

What path difference corresponds to waves arriving in antiphase?

An odd number of half-wavelengths.

What is the condition for destructive interference in terms of path difference?

Path difference = (2n + 1)λ/2, where n = 0, 1, 2, ...

What is the condition for destructive interference in terms of phase difference?

Phase difference = (2n + 1)π rad.

What path difference produces the first destructive interference minimum?

λ/2.

What path difference produces the next destructive interference minimum?

3λ/2.

What path difference produces the next one after 3λ/2?

5λ/2.

What path differences produce constructive interference?

0, λ, 2λ, 3λ, ... .

What path differences produce destructive interference?

λ/2, 3λ/2, 5λ/2, ... .

What phase difference corresponds to a path difference of zero?

0 rad.

What phase difference corresponds to a path difference of λ/4?

π/2 rad or 90°.

What phase difference corresponds to a path difference of λ/2?

π rad or 180°.

What phase difference corresponds to a path difference of 3λ/4?

3π/2 rad or 270°.

What phase difference corresponds to a path difference of λ?

2π rad or 360°.

What phase difference corresponds to a path difference of 1.5λ?

3π rad or 540°.

How can path difference be converted into phase difference in radians?

Phase difference = 2π × (path difference/λ).

How can path difference be converted into phase difference in degrees?

Phase difference = 360° × (path difference/λ).

How can phase difference be converted into path difference?

Path difference = (phase difference/2π)λ when phase is measured in radians.

If the path difference is 2λ, what type of interference occurs?

Constructive interference.

If the path difference is 2.5λ, what type of interference occurs?

Destructive interference.

If the path difference is 3λ, what type of interference occurs?

Constructive interference.

If the path difference is 3.5λ, what type of interference occurs?

Destructive interference.

At the central maximum of a double-slit pattern, what is the path difference?

Zero.

At the central maximum, what is the phase difference between the waves?

0 rad.

Why is the centre of a double-slit interference pattern bright?

The distances from the two slits are equal, so the path difference is zero and the waves arrive in phase.

What is the path difference at the first bright fringe next to the central maximum?

λ.

What is the phase difference at the first bright fringe next to the central maximum?

2π rad.

What is the path difference at the first dark fringe next to the central maximum?

λ/2.

What is the phase difference at the first dark fringe next to the central maximum?

π rad.

What happens to the fringe pattern if the screen is moved further away from the two slits?

The fringes become further apart.

Why does moving across an interference pattern change the resultant amplitude?

The distances from the two sources change, changing the path difference and therefore the phase difference.

What happens when two waves arrive at a point crest-to-crest?

They are in phase and interfere constructively.

What happens when a crest from one wave meets a trough from another equal-amplitude wave?

They are in antiphase and interfere destructively.

What is the relationship between path difference and constructive interference?

A whole-number path difference in wavelengths produces constructive interference.

What is the relationship between path difference and destructive interference?

An odd number of half-wavelengths produces destructive interference.

Why is interference considered evidence that light behaves as a wave?

Interference results from superposition, which is a characteristic wave behaviour.

What safety precaution should be taken when using a laser for two-slit interference?

Never look directly into the laser beam or direct it towards anyone's eyes.

What safety precaution is needed when using a ripple tank?

Keep electrical equipment away from water and do not handle electrical equipment with wet hands.