• 8.3.1 Understand the terms interference and coherence.
• Identify the conditions necessary for observable wave interference.
• Distinguish between constructive and destructive interference.
• Relate path difference and phase difference to the type of interference.

• Define interference and coherence in English using appropriate scientific vocabulary.
• Explain the conditions for constructive and destructive interference using terms like path difference, phase difference, wavelength, and amplitude.
• Discuss examples of interference phenomena.

Review the key terms using flashcards. You can find relevant sets on Quizlet or create your own:

Search for «Wave Interference & Coherence» flashcards on Quizlet

Focus on understanding the definition and application of each term.

Interference

The phenomenon that occurs when two or more waves meet while traveling along the same medium. This results in the formation of a new wave whose resultant displacementнәтижесіндегі ығысу / результирующее смещение is the algebraic sum of the displacements of the individual waves.

Translation (Қазақша)

Толқындардың бір ортада таралған кезде кездесуінен пайда болатын құбылыс. Бұл жағдайда пайда болған жаңа толқынның ығысуы жеке толқындардың ығысуларының алгебралық қосындысына тең болады.

Coherence

Two wave sourcesкөздері / источники are coherent if they emit waves with the same frequency and have a constant phase differenceтұрақты фаза айырымы / постоянная разность фаз between them. This is a crucial condition for observing a stable interference pattern.

Translation (Қазақша)

Егер екі толқын көзі бірдей жиіліктегі толқындар шығарса және олардың арасында тұрақты фаза айырымы болса, онда олар когерентті болып табылады. Бұл тұрақты интерференциялық көріністі бақылау үшін маңызды шарт.

Principle of Superposition

When two or more waves of the same type meet at a point, the resultant displacementнәтижесіндегі ығысу / результирующее смещение at that point is equal to the vector sum of the displacements of the individual waves.

Translation (Қазақша)

Бірдей типтегі екі немесе одан да көп толқындар бір нүктеде кездескенде, сол нүктедегі нәтижелік ығысу жеке толқындардың ығысуларының векторлық қосындысына тең болады.

Constructive Interference

Occurs when waves meet in phase (e.g., crest meets crest or trough meets trough), resulting in a wave with a larger amplitudeамплитуда / амплитуда. The path difference is an integer multiple of the wavelength (nλ).

Translation (Қазақша)

Толқындар фазада кездескенде (мысалы, шың шыңмен немесе ойыс ойыспен кездескенде) пайда болады, нәтижесінде амплитудасы үлкенірек толқын пайда болады. Жол айырымы толқын ұзындығының бүтін еселігіне тең (nλ).

Destructive Interference

Occurs when waves meet out of phase (e.g., crest meets trough), resulting in a wave with a smaller or zero amplitude. The path difference is a half-integer multiple of the wavelength ((n+1/2)λ).

Translation (Қазақша)

Толқындар фазадан тыс кездескенде (мысалы, шың ойыспен кездескенде) пайда болады, нәтижесінде амплитудасы кішірек немесе нөлге тең толқын пайда болады. Жол айырымы толқын ұзындығының жарты бүтін еселігіне тең ((n+1/2)λ).

What is Interference?

Interference is a phenomenon that occurs when two or more waves superposeқабаттасады, беттеседі / накладываются, суперпозиционируют and interact with each other. This interaction results in a new wave pattern where the resultant amplitudeнәтижелік амплитуда / результирующая амплитуда is the sum of the individual amplitudes based on the principle of superposition.

Interference can be constructive or destructive:

• Constructive interference occurs when waves meet in phase (e.g., a crest meets a crest, or a trough meets a trough). The amplitudes of the individual waves add together, resulting in a wave with a larger amplitude (greater intensity).
• Destructive interference occurs when waves meet out of phase (e.g., a crest meets a trough). The amplitude of one wave is subtracted from the other. If the waves have equal amplitudes, this can result in complete cancellation (zero amplitude, minimum intensity).

What is Coherence?

For a stable and observable interference pattern to occur, the wave sources must be coherent.

Two sources are coherent if:

1. They emit waves with the same frequencyжиілік / частота (and therefore the same wavelength).
2. They have a constant phase differenceфаза айырымы / разность фаз between them. This means the phase relationship between the waves does not change over time. If the phase difference were random, the interference pattern would fluctuate rapidly and not be observable.

Lasers are common examples of coherent light sources. Light from two separate filament lamps is incoherent because the random emission of photonsфотондардың кездейсоқ эмиссиясы / случайное излучение фотонов by many atoms means there’s no constant phase relationship between the light emitted from them.

Conditions for Observable Interference:

1. Coherent Sources: As explained above, the sources must maintain a constant phase difference and have the same frequency.
2. Similar Amplitudes: For good contrast between maxima (constructive interference) and minima (destructive interference), the interfering waves should have similar (preferably equal) amplitudes. If one wave is much stronger, its pattern will dominate, and the minima will not be very dark.
3. Same Type of Wave: Interference occurs between waves of the same type (e.g., light waves interfere with light waves, sound waves with sound waves).
4. Polarisation (for transverse waves): If the waves are transverse (like light waves) and polarisedполяризацияланған / поляризованные, they must generally be polarised in the same plane for interference to be observed effectively (or be unpolarised).

Path Difference and Phase Difference

The type of interference (constructive or destructive) occurring at a specific point depends on the path differenceжол айырымы / разность хода (Δx) and consequently the phase differenceфаза айырымы / разность фаз (Δφ) between the waves arriving at that point.

• Path difference (Δx): The difference in the distance travelled by the two waves from their respective sources to the point where interference is observed.
• Phase difference (Δφ): The difference in phase (in radians or degrees) between the two waves at that specific point.

The relationship between phase difference and path difference is given by: Δφ = (2π/λ) × Δx

For constructive interference (maximum intensity):

• Path difference, Δx = nλ (where n = 0, 1, 2, 3, …)
  
  (The waves arrive in phase)
• Phase difference, Δφ = 2nπ radians (or 0°, 360°, 720°, …)

For destructive interference (minimum intensity):

• Path difference, Δx = (n + 1/2)λ (where n = 0, 1, 2, 3, …)
  
  (The waves arrive in antiphase or 180° out of phase)
• Phase difference, Δφ = (2n + 1)π radians (or 180°, 540°, 900°, …)

Questions on Theory:

1. Easy: What are the two main types of wave interference, and what happens to the amplitude in each case?
   
   Answer

   The two main types are constructive and destructive interference. In constructive interference, the amplitudes add up, resulting in a larger amplitude. In destructive interference, amplitudes subtract, resulting in a smaller or zero amplitude.
2. Medium: Explain why two light bulbs from different lamps are generally not coherent sources.
   
   Answer

   Light from bulbs is produced by many individual atoms emitting photons independently and randomly. This means there is no constant phase relationship between the waves emitted from two different bulbs (or even different parts of the same bulb filament). Their frequencies might also have slight, random variations. Therefore, they are not coherent.
3. Medium: Two coherent sources emit waves of wavelength λ = 0.2 m. If the path difference from these sources to a point P is 0.5 m, will constructive or destructive interference occur at P? Show your reasoning.
   
   Answer

   Given: Wavelength λ = 0.2 m, Path difference Δx = 0.5 m.
   To determine the type of interference, we find the ratio Δx / λ:
   Δx / λ = 0.5 m / 0.2 m = 2.5
   Since the path difference is 2.5λ, which can be written as (2 + 1/2)λ, this matches the condition for destructive interference (Δx = (n + 1/2)λ, where n=2).
   Therefore, destructive interference will occur at point P.
   
4. Hard (Critical Thinking): Imagine you are trying to demonstrate interference with sound waves using two loudspeakers. If one loudspeaker is accidentally connected with its terminals reversed (out of phase by 180° or π radians compared to the other, relative to the input signal), how would this affect the conditions for constructive and destructive interference based on path difference?
   
   Answer

   If one loudspeaker is connected with reversed terminals, it introduces an initial phase difference of π radians (180°) between the waves emitted by the two sources, even before considering path difference.
   Let’s say source 2 has this initial π phase shift.
   The total phase difference at a point P will be Δφ_total = (2π/λ)Δx + π.

   For constructive interference, Δφ_total must be 2mπ (where m is an integer).
   So, (2π/λ)Δx + π = 2mπ
   (2π/λ)Δx = (2m — 1)π
   Δx = (2m — 1)λ/2 = (m — 1/2)λ.
   This means constructive interference will now occur where path difference is a half-integer multiple of wavelength (e.g., 0.5λ, 1.5λ, etc.), which was previously the condition for destructive interference.

   For destructive interference, Δφ_total must be (2m + 1)π.
   So, (2π/λ)Δx + π = (2m + 1)π
   (2π/λ)Δx = 2mπ
   Δx = mλ.
   This means destructive interference will now occur where path difference is an integer multiple of wavelength (e.g., 0, λ, 2λ, etc.), which was previously the condition for constructive interference.

   In essence, the conditions for constructive and destructive interference based on path difference are swapped.
   

Activity 1: Fill in the Blanks

Complete the sentences below using the key terms from the lesson:

1. For observable interference, wave sources must be ______________, meaning they have the same ______________ and a constant ______________ ______________.
2. When waves meet crest to crest, or trough to trough, they are in phase, and ______________ interference occurs.
3. If waves meet crest to trough, they are out of phase, and ______________ interference occurs, potentially leading to cancellation.
4. The ______________ of ______________ states that the resultant displacement at a point where waves meet is the vector sum of their individual displacements.
5. The difference in distance travelled by two waves from their sources to a specific point is called the ______________ ______________.

Activity 2: True or False?

1. Coherent waves must have the same amplitude. (True/False)
2. Interference can only occur with light waves. (True/False)
3. If the path difference is equal to one full wavelength, constructive interference occurs. (True/False)
4. A phase difference of π radians corresponds to destructive interference if the waves initially had zero phase difference. (True/False)
5. Two independent lasers are always coherent with each other. (True/False)

This video provides a visual explanation of interference and coherence:

Further Viewing — Related Topics:

• Young’s Double Slit Experiment (Khan Academy) — A classic demonstration of light interference.
• How Noise Cancelling Headphones Work (Veritasium) — An application of destructive interference.
• Interference of Waves — A Level Physics (Flipping Physics)

Example 1: Sound Wave Interference

Two coherent loudspeakers, S₁ and S₂, are separated by a small distance and emit sound waves of wavelength λ = 0.75 m. A microphone is placed at point P. The distance S₁P is 3.00 m and S₂P is 3.375 m.

(a) Calculate the path difference at point P.

(b) Determine the type of interference (constructive or destructive) occurring at P. Explain your reasoning.

Example 2: Light Wave Interference and Phase Difference

Two coherent light sources produce an interference pattern. At a point Q, the path difference between the waves arriving from the two sources is 9.0 × 10^-7 m. The wavelength of the light is λ = 6.0 × 10^-7 m.

(a) Calculate the phase difference between the waves arriving at point Q in radians.

(b) State whether constructive or destructive interference occurs at point Q.

Explore wave interference using the PhET Interactive Simulation.

Link to Simulation: PhET Wave Interference Simulation

Instructions:

1. Open the simulation and select the «Interference» tab.
2. Choose «Light» from the wave options (top left, click the water tap icon to change).
3. Turn on two light sources by clicking the green button on the second laser.
4. Observe the pattern of bright and dark fringes on the screen. You can use the «Screen» and «Intensity Graph» tools.

Tasks:

1. Task 1: Adjust the frequency of the light using the slider. How does the spacing between the bright fringes in the interference pattern change as you increase the frequency? What about when you decrease it?
2. Task 2: Reset the frequency. Now, adjust the separation between the two light sources (slit separation). How does the fringe spacing change as you increase the separation? What about when you decrease it?
3. Task 3: Reset the settings. What happens to the contrast (how distinct the bright and dark fringes are) if you make the amplitude of one source significantly smaller than the other (use the amplitude sliders for each source)?

Work with a partner or in a small group for this activity.

Option 1: LearningApps.org Activity

Go to the following LearningApps.org activity to test your understanding of interference and related terms:

Interference and Diffraction — Matching Activity

Discuss your answers with your partner(s) and clarify any concepts you are unsure about.

Option 2: Quizizz Challenge

Your instructor may provide a link to a Quizizz game on Wave Interference. Alternatively, you can search for one:

1. Go to Quizizz Join Page.
2. Your instructor will provide a game code, or you can search for public quizzes on «Wave Interference Physics» or «Coherence and Interference».
3. Compete with your classmates and review the answers to solidify your understanding.

Discussion Points for your group:

• What are the key differences between constructive and destructive interference?
• Why is coherence essential for observing a clear interference pattern?
• Can you think of a real-world example (not already mentioned) where wave interference is important?

Answer the following questions to test your understanding and ability to apply the concepts of interference and coherence. Show your working where necessary.

1. Two coherent radio antennas, A and B, are separated by a distance of 120 m. They transmit signals in phase with a wavelength of 30 m. A car is driving along a straight road that is parallel to the line AB and 500 m away from it.

   (a) Calculate the frequency of the radio waves.

   (b) Consider a point P on the road directly opposite the midpoint of AB. Explain, with reasoning, the type of interference occurring at P.

   (c) Another point Q on the road is such that QA = 510 m and QB = 540 m. Determine the type of interference occurring at Q.

   (d) If the phase of antenna B was shifted by π radians (180°) relative to antenna A, how would your answer to part (b) change? Explain.

2. Explain in detail what is meant by ‘coherence’ when referring to two wave sources. Why are two independent filament lamps unlikely to produce a visible interference pattern, whereas two images of the same small source (e.g., via a double slit) can?

3. A student is investigating the interference of sound waves using two loudspeakers connected to the same signal generator. The loudspeakers are placed 2.0 m apart. The student walks in a line parallel to the line joining the loudspeakers, at a distance of 5.0 m away. The speed of sound is 340 m s^-1 and the frequency of the sound is 680 Hz.

   (a) Calculate the wavelength of the sound waves.

   (b) Explain why the student hears a series of loud and quiet sounds as she walks along the line.

   (c) Calculate the path difference required for the first position of destructive interference from the central maximum.

4. Describe how the principle of superposition leads to the phenomena of constructive and destructive interference. Use diagrams to illustrate how waves combine in both cases, showing the resultant wave.

5. Interference is not only observed with light and sound but also with matter waves, such as electrons. Briefly explain what this observation implies about the nature of particles like electrons. What conditions would be necessary to observe interference effects with electrons passing through two narrow slits?

(Note: These questions are designed for analysis and synthesis. Focus on clear explanations and accurate calculations.)

• Save My Exams — Interference: CIE A-Level Physics — Interference Notes
• PhysicsAndMathsTutor — Interference: A-Level CIE Physics — Interference
• OpenStax University Physics — Interference: Chapter 3: Interference (University Physics Vol 3)
• HyperPhysics — Coherence: HyperPhysics — Coherence Concept
• YouTube — The Original Double Slit Experiment: Veritasium — The Original Double Slit Experiment (Provides historical context and clear explanations)

Take a few moments to reflect on what you have learned in this lesson:

1. What are the two most important concepts or facts you learned about interference and coherence today?
2. Which part of today’s lesson (e.g., theory, examples, simulation) did you find most challenging, and why? What could help you overcome this challenge?
3. How can understanding wave interference be useful or applied in real-world technologies or phenomena? Try to think of one example not discussed in detail.
4. On a scale of 1 (Not at all understood) to 5 (Very well understood), how would you rate your current understanding of interference and coherence?
5. What specific steps can you take to improve your understanding if your rating was below 4? (e.g., re-watch a video, try more problems, ask a question).