To tackle the question regarding stationary waves, let's break down both the assertion and the reason provided. The assertion states that in stationary waves, there is no transfer of energy, while the reason claims that the ratio of kinetic energy to potential energy is independent of position. We need to analyze these statements to determine their truthfulness and the relationship between them.
Analyzing the Assertion
The assertion that "in stationary waves, there is no transfer of energy" is indeed true. In stationary waves, also known as standing waves, the wave does not propagate through space. Instead, it oscillates in place, creating nodes (points of no displacement) and antinodes (points of maximum displacement). Because the energy is not moving from one point to another, we can conclude that there is no net transfer of energy along the medium.
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 kinetic energy (due to the motion of particles) and potential energy (due to the displacement of particles from their equilibrium position) oscillate in a specific manner. The ratio of these energies remains constant throughout the wave, regardless of the position along the wave. This is a characteristic feature of stationary waves.
Connecting the Dots
Now, we need to determine if 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 lack of energy transfer is primarily due to the nature of the wave being stationary, characterized by fixed nodes and antinodes, rather than the ratio of kinetic to potential energy being constant.
Conclusion on the Options
Given this analysis, we can conclude that:
- Both the assertion and the reason are true.
- The reason does not explain the assertion.
Therefore, the correct answer is (b): If both the assertion and reason are true but reason does not explain the assertion.
Further Insights
To deepen your understanding, consider the analogy of a swing. When you push a swing, it moves back and forth (like a wave), transferring energy as it moves. In contrast, a stationary wave can be likened to a swing that is held at a fixed point, oscillating without moving forward or backward. This illustrates the concept of energy being present but not transferred in stationary waves.
