Assertion -In a standing waves x - 0 is a node- Then total mechanical energy lying between x - 0 and x - -8 is not equal to the energy lying between x - -8 and x - -4 Reason- In standing waves different particles oscillate with different amplitudes-

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Assertion :In a standing waves x = 0 is a node. Then total mechanical energy lying between x = 0 and $x = \frac{λ}{8}$ is not equal to the energy lying between $x = \frac{λ}{8}$ and $x = \frac{λ}{4}$ Reason: In standing waves different particles oscillate with different amplitudes.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
In a standing wave, the velocities of different particles is a function of the slope at that point. Since, the slope is not constant as the wave goes along, therefore the particle velocities are not the same either. Hence, the total mechanical energies are different

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Assertion :In a standing waves x = 0 is a node. Then total mechanical energy lying between x = 0 and x=λ8 is not equal to the energy lying between x=λ8 and x=λ4 Reason: In standing waves different particles oscillate with different amplitudes.

Assertion :In a standing waves x = 0 is a node. Then total mechanical energy lying between x = 0 and $x = \frac{λ}{8}$ is not equal to the energy lying between $x = \frac{λ}{8}$ and $x = \frac{λ}{4}$ Reason: In standing waves different particles oscillate with different amplitudes.