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.

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 the position.

Understanding Stationary Waves

Stationary waves, also known as standing waves, occur when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This results in a wave pattern that appears to be stationary, with certain points (nodes) remaining at rest and others (antinodes) oscillating with maximum amplitude.

Assertion Analysis

The assertion that there is no transfer of energy in a stationary wave is indeed true. In stationary waves, energy is not transmitted through the medium; instead, it is localized around the nodes and antinodes. The energy oscillates between kinetic and potential forms but does not propagate away from the wave's source.

Reason Evaluation

Now, let's consider the reason provided: the ratio of kinetic energy to potential energy being independent of position. This statement is somewhat misleading. In a stationary wave, while the total energy oscillates between kinetic and potential forms, the ratio does vary depending on the position along the wave. At the nodes, the kinetic energy is zero, while at the antinodes, the potential energy is zero. Therefore, the ratio of kinetic to potential energy is not constant throughout the wave.

Conclusion on the Relationship

Given this analysis, we can conclude the following:

• The assertion is true: there is no transfer of energy in a stationary wave.
• The reason is false: the ratio of kinetic energy to potential energy does depend on the position within the wave.

Based on these evaluations, the correct answer to your question is (c): the assertion is true, but the reason is false. This understanding is crucial in the study of wave mechanics, as it highlights the unique characteristics of stationary waves compared to traveling waves, where energy transfer is a key feature.