When a standing wave is set up in a pipe which is open from one end, which of the following statements is true?
Correct answer: A. The open end of the pipe is a displacement antinode.
- A. The open end of the pipe is a displacement antinode.
- B. Wavelength = length string / number of nodes
- C. The shape of the string at any instant shows a symmetry about the midpoint of the string
- D. Frequency = number of nodes x fundamental frequency
Explanation
For a standing wave set up in a pipe that is open at one end, the correct statement is:A. Sum of the number of antinodes and the number of nodes is always odd.In a pipe open at one end, standing waves can form due to the reflection of waves at the closed end and the formation of antinodes and nodes along the length of the pipe. An antinode is a point of maximum displacement, while a node is a point of zero displacement. When a standing wave is set up in the pipe, there will always be one node at the closed end (due to fixed boundary conditions) and varying numbers of nodes and antinodes along the length of the pipe, depending on the mode of vibration. In this case, the sum of the number of antinodes and the number of nodes will always be an odd number. This is because there is always one more node than antinode in a standing wave in a pipe open at one end.
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About Stationary Waves
Stationary waves form when two waves of the same frequency and amplitude travel in opposite directions and interfere. The topic covers nodes, antinodes, wavelength, phase, resonance, and the allowed frequencies on strings and in air columns. Unlike progressive waves, stationary waves do not transfer energy from one point to another.
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