Question 405: Waves

Question

Consider the following statements about stationary waves.
A. The distance between two adjacent nodes or antinodes is equal to $$\frac{\lambda}{2}(\lambda=$$ wavelength of the wave)
B. A node is always formed at the open end of the open organ pipe.
Choose the correct option from the following.

Accepted Answer

The correct option is C: Only the statement A is true.
Statement A is indeed correct. In a stationary wave, or standing wave, nodes are points of zero amplitude, while antinodes are points of maximum amplitude. The distance between two adjacent nodes or two adjacent antinodes is half the wavelength of the wave, or $$\frac{\lambda}{2}$$. This is because one complete wavelength of the wave contains two node-to-node or antinode-to-antinode segments.
Statement B, however, is incorrect. A node represents a point of no displacement in a standing wave and is typically formed where there is a fixed end that cannot vibrate, like a clamped end of a string. In contrast, an open end of an organ pipe is free to move and thus supports an antinode, not a node. The pressure variation at an open end is minimal (corresponding to a displacement antinode), while pressure variations are maximal at a closed end (corresponding to a displacement node). Therefore, in an open organ pipe, there's actually an antinode at each open end if we're discussing a standing wave in terms of displacement rather than pressure.

Answer

Both statements A and B are wrong.

Answer

Only the statement B is true.

Answer

Only the statement A is true.

Answer

Both statements A and B are true.

Waves

Consider the following statements about stationary waves. A. The distance between two adjacent nodes or antinodes is equal to $\frac{\lambda}{2}(\lambda=$ wavelength of the wave) B. A node is always formed at the open end of the open organ pipe. Choose the correct option from the following.

Choose the correct answer: