Wave Phase and Superposition

The Behaviour of Waves

Define phase.

The position of a point within a complete cycle of an oscillation or wave.

How is phase usually measured?

As an angle in degrees (°) or radians (rad).

What phase angle represents one complete cycle?

360° or 2π rad.

What phase angle represents 1/4 of a cycle?

90° or π/2 rad.

What phase angle represents 1/2 of a cycle?

180° or π rad.

What phase angle represents 3/4 of a cycle?

270° or 3π/2 rad.

What phase angle represents one whole cycle?

360° or 2π rad.

What phase angle represents 1.5 cycles?

540° or 3π rad.

What distance corresponds to a phase difference of 90°?

λ/4.

What distance corresponds to a phase difference of 180°?

λ/2.

What distance corresponds to a phase difference of 270°?

3λ/4.

What distance corresponds to a phase difference of 360°?

λ.

What is meant by phase difference?

The difference in phase between two points or two waves.

What is the phase difference between two adjacent crests?

360° or 2π rad, equivalent to 0° phase difference.

What is the phase difference between a crest and the next trough?

180° or π rad.

What does it mean for two points to be in phase?

They are at the same point in their oscillation cycle and moving in the same direction.

What is the phase difference between two points that are in phase?

0° or an integer multiple of 360°.

What does it mean for two waves to be in antiphase?

They have a phase difference of 180° or π rad.

How can phase angles greater than 360° be simplified?

Subtract complete cycles of 360° until the equivalent phase within one cycle is found.

What is the equivalent phase of 450°?

90°.

What is 450° in radians?

5π/2 rad.

Why can 450° and 90° represent the same phase?

They differ by one complete cycle of 360°.

Define a wavefront.

A line connecting points on a wave that are at exactly the same phase.

What phase difference exists between all points on the same wavefront?

0°, or equivalently a whole number of complete cycles.

What does a wavefront represent physically?

A set of points on a wave that are at the same stage of their oscillation.

How are wavefronts commonly drawn?

As lines joining points of equal phase, such as wave crests.

What is a ray in wave diagrams?

A line showing the direction of wave travel.

What is the relationship between rays and wavefronts?

Rays are perpendicular to wavefronts.

Define superposition.

When two or more waves are in the same location, the resultant displacement is the vector sum of their individual displacements.

What is the principle of superposition?

When waves overlap, their individual displacements add together to give the resultant displacement.

What happens to waves after they superpose?

They continue travelling in their original directions.

Are waves permanently changed when they superpose?

No. After overlapping, they continue travelling as before.

What happens when two positive wave pulses meet?

Their displacements add to produce a larger positive displacement.

If two upward pulses of amplitudes A and B completely overlap, what is the resultant amplitude?

A + B.

What happens when a positive and negative displacement overlap?

Their displacements subtract because displacement is a vector.

What is constructive interference?

The superposition of waves that are in phase, producing a resultant wave of greater amplitude.

When does constructive interference occur?

When waves meet in phase.

What is the phase difference for complete constructive interference?

0°, 360°, 720°, etc., or 0, 2π, 4π rad, etc.

What happens when two identical waves interfere completely constructively?

The resultant amplitude is twice the amplitude of either individual wave.

If two identical waves of amplitude A meet in phase, what is the resultant amplitude?

2A.

What is destructive interference?

The superposition of waves that are out of phase, producing a smaller resultant amplitude.

When does complete destructive interference occur for two identical waves?

When they are exactly 180° or π rad out of phase.

What is the phase difference for complete destructive interference?

180° or π rad, or an odd multiple of these.

What happens when two identical waves interfere completely destructively?

Their displacements cancel and the resultant amplitude is zero.

If two identical waves of amplitude A meet exactly 180° out of phase, what is the resultant amplitude?

Zero.

Why can two waves cancel during destructive interference?

At each point, one wave has an equal positive displacement while the other has an equal negative displacement, so their vector sum is zero.

Does destructive interference destroy the energy of the individual waves?

No. The waves continue to propagate after they have passed through each other.

What is interference?

The result of the superposition of two or more waves.

What determines whether interference is constructive or destructive?

The phase difference between the waves.

What happens when waves are partially out of phase?

They partially reinforce or cancel, producing an intermediate resultant amplitude.

What phase relationship is required for maximum constructive interference?

The waves must be in phase.

What phase relationship is required for complete destructive interference between identical waves?

The waves must be in antiphase.

How can many small water waves temporarily produce a very large wave?

If many waves arrive at the same location in phase, their displacements add by superposition.

Why can a very large wave formed by superposition disappear quickly?

The individual waves continue travelling past one another, so the constructive superposition is only temporary.

How is superposition applied to continuous waves?

At every point where the waves overlap, their instantaneous displacements are added.

What is the resultant wave?

The wave produced by adding the displacements of overlapping waves.

What is the difference between a wavefront and a ray?

A wavefront joins points with the same phase, whereas a ray shows the direction of wave travel.

What is the phase difference between two crests separated by one wavelength?

360° or 2π rad, equivalent to being in phase.

What is the phase difference between points separated by half a wavelength?

180° or π rad.

What is the phase difference between points separated by a quarter wavelength?

90° or π/2 rad.

What is the phase difference between points separated by three-quarters of a wavelength?

270° or 3π/2 rad.

How can phase difference be calculated from separation along a wave?

Phase difference = (separation ÷ wavelength) × 360°.

How can phase difference in radians be calculated from separation along a wave?

Phase difference = (separation ÷ wavelength) × 2π.