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Assertion: Standing waves are formed whe...

Assertion: Standing waves are formed when amplitudes of two constituent waves are equal.
Reason: At any point net displacement at a given time is resultant of displacement of constituent waves.

A

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

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The correct Answer is:
To analyze the given assertion and reason, we can break down the problem step by step: ### Step 1: Understanding the Assertion The assertion states that "Standing waves are formed when amplitudes of two constituent waves are equal." - **Analysis**: Standing waves are formed due to the superposition of two waves traveling in opposite directions. While having equal amplitudes can lead to a standing wave, it is not a necessary condition. Standing waves can also form with waves of different amplitudes as long as their wavelengths, frequencies, and velocities are the same. ### Step 2: Conclusion on the Assertion Since standing waves can be formed with different amplitudes, the assertion is **false**. ### Step 3: Understanding the Reason The reason states that "At any point, net displacement at a given time is the resultant of the displacement of constituent waves." - **Analysis**: This statement is true. The net displacement of a wave at any point is indeed the sum of the displacements caused by each of the constituent waves. For two waves, this can be mathematically expressed as: \[ y_{\text{net}} = y_1 + y_2 \] where \( y_1 \) and \( y_2 \) are the displacements of the two waves. ### Step 4: Conclusion on the Reason The reason is **true** because it accurately describes how the net displacement of waves is determined by the superposition principle. ### Final Conclusion - The assertion is **false**. - The reason is **true**. ### Summary - **Assertion**: False - **Reason**: True
To analyze the given assertion and reason, we can break down the problem step by step: ### Step 1: Understanding the Assertion The assertion states that "Standing waves are formed when amplitudes of two constituent waves are equal." - **Analysis**: Standing waves are formed due to the superposition of two waves traveling in opposite directions. While having equal amplitudes can lead to a standing wave, it is not a necessary condition. Standing waves can also form with waves of different amplitudes as long as their wavelengths, frequencies, and velocities are the same. ### Step 2: Conclusion on the Assertion ...
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