A pipe is open at both ends. A stationary wave is formed in the air of the pipe. Which statement is true?
Correct answer: D. The sum of number of nodes and the number of antinodes is always an odd number
- A. There is always a central antinod
- B. There is always a central node
- C. The sum of number of nodes and the number of antinodes is always an even number
- D. The sum of number of nodes and the number of antinodes is always an odd number
Explanation
Option A: This statement is false. In a pipe open at both ends, there is no central antinode. The antinodes are located at the open ends of the pipe.Option B: There is always a central node: This statement is true. In a pipe open at both ends, there is always a central node where the displacement of the air particles is minimum. This node is located at the midpoint of the pipe.Option C: The sum of the number of nodes and the number of antinodes is always an even number: This statement is false. In a pipe open at both ends, the number of nodes and the number of antinodes are not always equal. The sum of the number of nodes and antinodes can be an odd number or an even number depending on the specific conditions and mode of the stationary wave.Option D: The sum of the number of nodes and the number of antinodes is always an odd number: This statement is true. In a pipe open at both ends, the sum of the number of nodes and the number of antinodes is always an odd number for any specific mode of the stationary wave. This is a characteristic property of such systems.
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Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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