Assertion : In stationary wave, there is
no transfer of energy.
Reason : The ratio of kinetic energy to
potential energy is independent of the
position.

(a) If both the assertion and reason are true and
reason explains the assertion.
(b) If both the assertion and reason are true but
reason does not explain the assertion.
(c) If as ser tion is true but rea son is false.
(d) If assertion is false but reason is true.

Please explain the solution in detail

To tackle the assertion and reason you've presented, let's break down both statements and analyze their validity and relationship. The assertion states that in a stationary wave, there is no transfer of energy, while the reason claims that the ratio of kinetic energy to potential energy is independent of position.

Analyzing the Assertion

The assertion about stationary waves is indeed true. In stationary waves, also known as standing waves, the wave pattern does not propagate through space. Instead, it consists of nodes (points of no displacement) and antinodes (points of maximum displacement). Because the energy is stored in the wave and oscillates between kinetic and potential forms without moving from one place to another, there is no net transfer of energy along the medium. This is a key characteristic of stationary waves.

Examining the Reason

The reason provided states that the ratio of kinetic energy to potential energy is independent of position. This statement is also true for stationary waves. In a stationary wave, at any given point, the energy oscillates between kinetic and potential forms, but the overall ratio remains constant throughout the wave. For instance, at the antinodes, kinetic energy is maximum while potential energy is minimum, and vice versa at the nodes. However, the ratio of these energies does not change as you move along the wave.

Connecting the Dots

Now, let's consider whether the reason explains the assertion. While both statements are true, the reason does not directly explain why there is no transfer of energy in stationary waves. The assertion is based on the nature of stationary waves, while the reason discusses the energy distribution without addressing the concept of energy transfer directly.

Conclusion on the Options

Given this analysis, the correct choice is (b): both the assertion and reason are true, but the reason does not explain the assertion. The assertion stands on the principle of stationary waves, while the reason provides information about energy ratios without linking it to the lack of energy transfer.

Summary

• Assertion: True - No energy transfer in stationary waves.
• Reason: True - Energy ratio is constant, but does not explain the assertion.
• Correct Option: (b) Both true, reason does not explain assertion.