Wave Behavior - Interference
Section: Physics | Syllabus: Cambridge Lower Secondary Checkpoint Science (0893)
Introduction to Interference
- Interference is what happens when two or more waves meet and combine together – their amplitudes add up to create a new wave pattern
- This is a fundamental property of all waves, whether they're water waves on a pond, sound waves in air, light waves, radio waves, or seismic waves in the Earth
- Wave characteristics review – these properties determine how waves interact when they meet:
- Amplitude: the maximum displacement from the rest position (height of peaks or depth of troughs)
- Peak (crest): the highest point of a wave
- Trough: the lowest point of a wave
- Wavelength: the distance between two consecutive peaks (or troughs)
- Frequency: how many waves pass a point per second
The Superposition Principle
- When two waves meet at the same point at the same time, their amplitudes add together, creating a resultant wave (the combined wave)
- After interfering, the waves continue traveling as if nothing happened – the type of interference depends on how the waves align
- Superposition is the principle that when waves overlap, the total displacement at any point is the sum of the displacements from each individual wave
- When waves overlap, they don't bounce off each other or stop – instead, they pass through each other and combine temporarily
Worked Example: Finding a Missing Component Wave
Sometimes you are given the resultant wave and only one of the two waves that combined to make it, and asked to draw the other (missing) wave.
- Step 1: remember the superposition rule works both ways - if wave B and wave C interact to make resultant wave A, then at every point, displacement of A = displacement of B + displacement of C
- Step 2: rearrange to find the missing wave. Displacement of C = displacement of A − displacement of B
- Step 3: at each point along the waves, subtract the known wave's displacement from the resultant wave's displacement to find the missing wave's displacement, then plot these points to draw waveform C
- Step 4: check your answer - superposing (adding) your drawn wave C back onto wave B should reproduce the original resultant wave A
Conditions for Clear Interference
For clear interference patterns to occur, waves should have similar frequencies and maintain a constant phase relationship (called coherent sources). Similar amplitudes also help create more observable effects.
- Similar frequencies – waves with very different frequencies create complex, hard-to-predict patterns
- Constant phase relationship – the waves maintain a consistent relationship as they travel
- Similar amplitudes – for the best observable effects
Constructive Interference
- Constructive interference occurs when two waves meet in phase (aligned so that peaks meet peaks and troughs meet troughs). Their amplitudes add together to create a wave with larger amplitude
- This creates regions of reinforcement, where the wave is stronger than the individual waves would be on their own
How Amplitudes Add Together
When waves are in phase, their displacements add algebraically. If both waves have positive displacement (peaks), they create an even larger positive displacement. If both have negative displacement (troughs), they create a deeper trough.
Worked Example: Peaks Meeting Peaks
Two waves meet at a point: Wave 1 has amplitude +3 cm (at a peak) and Wave 2 has amplitude +3 cm (also at a peak).
- Step 1: add the amplitudes. +3 cm + 3 cm
- Step 2: calculate the resultant amplitude. +6 cm
- Step 3: interpret. The combined wave has double the amplitude – the peak is twice as high
Worked Example: Troughs Meeting Troughs
Two waves meet at a point: Wave 1 has amplitude -2 cm (at a trough) and Wave 2 has amplitude -2 cm (also at a trough).
- Step 1: add the amplitudes. -2 cm + (-2 cm)
- Step 2: calculate the resultant amplitude. -4 cm
- Step 3: interpret. The trough becomes deeper – the combined wave has larger amplitude in the negative direction
Characteristics of Constructive Interference
- The resultant wave is bigger/stronger than either original wave
- Peaks become higher and troughs become deeper
- The wave carries more energy at these points
- For sound waves, this creates louder sound
Application: Sound Reinforcement
- When sound waves from two speakers interfere constructively, the sound is louder than from one speaker alone. This happens when the sound waves arrive at a location with their peaks aligned
- At concerts with multiple speakers, some spots in the audience experience constructive interference. These are called "sweet spots" where the music sounds noticeably louder and fuller
- The louder sound from constructive interference doesn't violate energy conservation – the energy is simply redistributed, so louder in some places means quieter in others (destructive interference)
Destructive Interference
- Destructive interference occurs when two waves meet out of phase (misaligned so that peaks meet troughs, specifically 180° out of phase – exactly opposite). Their amplitudes cancel out to create a wave with reduced or zero amplitude
- This creates regions of cancellation, where the wave is weaker than the individual waves or may disappear entirely
How Amplitudes Cancel Out
When waves are out of phase, their displacements have opposite signs and subtract from each other. A positive displacement (peak) meets a negative displacement (trough), reducing the total displacement.
Worked Example: Perfect Cancellation
Two waves meet at a point: Wave 1 has amplitude +3 cm (at a peak) and Wave 2 has amplitude -3 cm (at a trough).
- Step 1: add the amplitudes. +3 cm + (-3 cm)
- Step 2: calculate the resultant amplitude. 0 cm
- Step 3: interpret. Complete cancellation – the waves completely cancel each other out, creating zero displacement
Worked Example: Partial Cancellation
Two waves meet at a point: Wave 1 has amplitude +4 cm (at a peak) and Wave 2 has amplitude -2 cm (at a trough).
- Step 1: add the amplitudes. +4 cm + (-2 cm)
- Step 2: calculate the resultant amplitude. +2 cm
- Step 3: interpret. Partial cancellation – the resultant wave is smaller than the larger original wave
Characteristics of Destructive Interference
- The resultant wave is smaller/weaker than the original waves
- In perfect destructive interference, the wave disappears completely (zero amplitude)
- The displacement returns to zero (flat line)
- No energy is destroyed – it's redistributed to other locations. Even though the wave "disappears" at certain points, the energy is redistributed to other locations where constructive interference occurs
Application: Sound Cancellation
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