Four organ pipes are described below. Which one has the highest frequency fundamental?
Correct answer: C. A 1.6 m pipe with both ends open
- A. A 2.3 m pipe with one end open and the other closed
- B. A 3.3 m pipe with one end open and the other closed
- C. A 1.6 m pipe with both ends open
- D. A 3.0 m pipe with both ends open
Explanation
The fundamental frequency of a pipe is determined by whether it is open or closed at its ends. A pipe open at both ends supports a half-wave resonant frequency, while a pipe closed at one end supports a quarter-wave resonant frequency. The frequency is inversely proportional to the length of the pipe. Therefore, the shorter the pipe, the higher the fundamental frequency. Option C, a 1.6 m pipe with both ends open, will have the highest frequency because it is the shortest among the pipes that allow a half-wave resonance. The other options are either longer or closed at one end, resulting in lower fundamental frequencies.
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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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