**Correct Option: B. The amplitude of the resultant wave is the sum of the amplitudes of the individual waves at each point in space.** ### Detailed Explanation: The principle of superposition is a fundamental concept in wave theory that describes how waves interact with each other. When two or more waves meet at a point in space, they combine to form a new wave. This combination is described by the principle of superposition, which states that the resultant wave's amplitude at any point is equal to the sum of the amplitudes of the individual waves at that same point. #### Step-by-Step Breakdown: 1. **Understanding Amplitude**: - Amplitude refers to the maximum displacement of points on a wave from its rest position. In simpler terms, it is how "tall" or "deep" the wave is. 2. **Constructive and Destructive Interference**: - When two waves meet, they can interfere in two main ways: - **Constructive Interference**: This occurs when the peaks (crests) of two waves align, resulting in a wave with a larger amplitude. For example, if Wave 1 has an amplitude of 3 units and Wave 2 has an amplitude of 2 units, the resultant wave will have an amplitude of 5 units (3 + 2). - **Destructive Interference**: This occurs when the crest of one wave aligns with the trough (lowest point) of another wave, which can reduce the overall amplitude. If Wave 1 has an amplitude of 3 units and Wave 2 has an amplitude of 2 units but is inverted (negative), the resultant wave will have an amplitude of 1 unit (3 - 2). 3. **Mathematical Representation**: - If we denote the amplitudes of two waves as \( A_1 \) and \( A_2 \), the resultant amplitude \( A_r \) can be expressed as: \[ A_r = A_1 + A_2 \] - This equation holds true at every point in space where the waves overlap. 4. **Implications of Superposition**: - The principle of superposition applies to all types of waves, including sound waves, light waves, and water waves. It is crucial for understanding phenomena such as interference patterns, standing waves, and resonance. ### Why Other Options Are Incorrect: - **Option A: Waves can only interfere constructively.** - This statement is incorrect because waves can interfere both constructively and destructively. The principle of superposition encompasses both types of interference, not just constructive. - **Option C: Waves cannot pass through one another.** - This is also incorrect. Waves can and do pass through one another. When they overlap, they temporarily combine according to the principle of superposition, but they continue to propagate independently after the interaction. - **Option D: The speed of a wave is constant regardless of the medium through which it travels.** - This statement is misleading. The speed of a wave depends on the medium it travels through. For example, sound travels faster in water than in air, and light travels at different speeds in different materials. The principle of superposition does not address wave speed but rather how waves interact. ### Common Pitfalls: - Students often confuse constructive and destructive interference, leading to incorrect conclusions about resultant amplitudes. - It’s important to remember that the principle of superposition applies at every point in space, not just at the peaks or troughs of the waves. ### Revision Summary: - The principle of superposition states that the resultant wave's amplitude is the sum of the individual wave amplitudes at each point. - Waves can interfere constructively (amplitudes add) or destructively (amplitudes subtract). - Waves can pass through one another and continue to propagate independently after interaction. - The speed of a wave varies with the medium, not constant across all media.