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Physics Chapter 9 : Topic 7
Superposition of Waves
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The principle of superposition states that when two or more waves overlap, the resultant displacement is:
Reasoning: According to the principle of superposition, the net displacement at any point is the algebraic sum of the displacements produced by individual waves.
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The principle of superposition is applicable when waves:
Reasoning: Superposition occurs when two or more waves travel through the same region of a medium.
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If two waves produce displacements of $\mathbf{+ \ 3\ cm}$ and $\mathbf{+ \ 5\ cm}$ at the same point, the resultant displacement is:
Reasoning: $\mathbf{y =}\mathbf{y}_{\mathbf{1}}\mathbf{+}\mathbf{y}_{\mathbf{2}}\mathbf{= 3 + 5 = 8\ }\mathbf{cm}$Both displacements are in the same direction.
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If two waves produce displacements of $\mathbf{+ \ 6\ cm}$ and $\mathbf{- \ 4\ cm}$ at a point, the resultant displacement is:
Reasoning: $\mathbf{y}\mathbf{= 6 +}\left( \mathbf{- \ 4} \right)\mathbf{= 2\ cm}$Opposite displacements partially cancel each other.
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Superposition of waves explains the formation of:
Reasoning: Interference occurs due to the superposition of two or more waves.
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Constructive interference occurs when two waves have:
Reasoning: Waves in the same phase add their amplitudes, producing maximum displacement.
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Destructive interference occurs when two waves have a phase difference of:
Reasoning: A phase difference of $\mathbf{180}^{\mathbf{o}}$ causes waves to oppose each other.
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Two waves of equal amplitude produce complete destructive interference when:
Reasoning: Equal and opposite displacements cancel completely.
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In constructive interference, the resultant amplitude is:
Reasoning: Amplitudes add when waves are in phase.
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In destructive interference, the resultant amplitude:
Reasoning: Opposing waves reduce the resultant displacement.
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Two waves have amplitudes $\mathbf{4\ cm\ }$and $\mathbf{6\ cm}$. The maximum possible resultantamplitude is:
Reasoning: For constructive interference: $\mathbf{A =}\mathbf{A}_{\mathbf{1}}\mathbf{+}\mathbf{A}_{\mathbf{2}}\mathbf{= 4 + 6 = 10\ }\mathbf{cm}$
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Two waves have amplitudes $\mathbf{8\ cm}$ and $\mathbf{5\ cm}$. The minimum possible resultant amplitude is:
Reasoning: For destructive interference: $\mathbf{A =}\left| \mathbf{8 - 5} \right|\mathbf{= 3\ cm}$
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Two waves with amplitudes $\mathbf{5\ cm}$ and $\mathbf{5\ cm}$ meet in opposite phases. The resultant amplitude is:
Reasoning: Equal amplitudes with $\mathbf{180}^{\mathbf{o}}$ phase difference cancel completely.
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Two waves overlap at a point. Their displacements are $\mathbf{7\ cm}$ and $\mathbf{- \ 9\ cm}$. Theresultant displacement is:
Reasoning: $\mathbf{7 + ( - \ 9) = - \ 2\ }\mathbf{cm}$
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A wave with displacement $\mathbf{10\ cm}$ combines with another wave havingdisplacement $\mathbf{10\ cm}$ in the same direction. The resultant displacement is:
Reasoning: Same-direction displacements add.
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Two waves are in phase when their phase difference is:
Reasoning: Zero phase difference means both waves reach maximum and minimum points together.
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Two waves are completely out of phase when their phase difference is:
Reasoning: A $\mathbf{180}^{\mathbf{o}}$ phase difference means one wave crest overlaps with another wave trough.
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If two waves have the same amplitude and frequency but opposite phases, they produce:
Reasoning: The waves cancel due to destructive interference.
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The resultant displacement depends on:
Reasoning: The final displacement depends on both magnitudes and directions of individual displacements.
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When waves overlap, each wave:
Reasoning: After interference, waves continue with their original properties.
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Beats are produced due to:
Reasoning: Beats result from alternating constructive and destructive interference.
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Noise-cancelling headphones work mainly due to:
Reasoning: They produce waves that cancel unwanted sound waves.
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The colors seen in thin films are due to:
Reasoning: Reflected light waves interfere to produce colors.
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The bright regions in an interference pattern are caused by:
Reasoning: Constructive interference increases intensity.
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The dark regions in an interference pattern are caused by:
Reasoning: Destructive interference reduces or cancels amplitude.
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If two waves meet and the resultant amplitude is greater than both individual amplitudes, the interference is:
Reasoning: Amplitude increases when waves add in phase.
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The principle of superposition applies because waves:
Reasoning: Waves can overlap and continue independently after interaction.
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A wave has amplitude $\mathbf{12\ cm}$ and another has amplitude $\mathbf{7\ cm}$. The resultant amplitude cannot be:
Reasoning: Maximum amplitude is $\mathbf{(12 + 7 = 19)\ cm}$.
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When two waves of equal amplitude interfere constructively, the intensity becomes:
Reasoning: Amplitude doubles, and intensity is proportional to amplitude squared.
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The principle of superposition is important because it explains:
Reasoning: Superposition is the foundation for understanding interference phenomena.
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