When a string is vibrating in a standing wave pattern , the power transmitted across an antinode , compared to the power transmitted across a node , is

Options

A. more
B. less
C. same (zero)
D. same( non - zero)

Explanation

To solve the question regarding the power transmitted across an antinode compared to the power transmitted across a node in a standing wave pattern, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Standing Waves**:
- A standing wave is formed by the superposition of two waves traveling in opposite directions with the same frequency, amplitude, and wavelength.

2. **Identifying Nodes and Antinodes**:
- In a standing wave, nodes are points where the displacement is always zero, while antinodes are points where the displacement reaches its maximum value.

3. **Energy and Power at Nodes and Antinodes**:
- At nodes, since the displacement is zero, the energy (and thus the power) transmitted is also zero. This is because power is related to the square of the amplitude of the wave.
- At antinodes, the displacement is maximum, indicating that the energy is also maximum. However, this does not mean that power is transmitted from the antinode to the node or vice versa.

4. **Power Transmission**:
- It is important to note that in a standing wave, there is no net power transmission along the medium. The energy oscillates between the nodes and antinodes, but there is no flow of power from one to the other.

5. **Conclusion**:
- Therefore, when comparing the power transmitted across an antinode to that across a node, we find that the power transmitted across both is effectively zero, as there is no net power flow in a standing wave.

### Final Answer:
The power transmitted across an antinode compared to the power transmitted across a node is the same (both are effectively zero).