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The world’s longest organ pipe, in the Boardwalk Hall Auditorium in Atlantic City, is 64 feet long. What is the fundamental frequency of this openopen
pipe?
The Correct Answer and Explanation is:
Correct Answer:
The fundamental frequency ff of an open-open pipe (open at both ends) is given by: f=v2Lf = \frac{v}{2L}
Where:
- vv is the speed of sound in air (typically 343 m/s343 \, \text{m/s} at 20°C),
- LL is the length of the pipe (64 feet = 19.51 meters, since 1 ft = 0.3048 m).
f=3432×19.51≈34339.02≈8.79 Hzf = \frac{343}{2 \times 19.51} \approx \frac{343}{39.02} \approx 8.79 \, \text{Hz}
Final Answer: Approximately 8.8 Hz
Explanation
Organ pipes produce sound by setting up standing waves in a column of air. The fundamental frequency (or first harmonic) is the lowest frequency at which the pipe naturally resonates. In an open-open pipe, both ends are open to the air, which means the air pressure at both ends must be atmospheric. This results in antinodes at both ends, and a node in the center.
For an open-open pipe, the length of the pipe is equal to half the wavelength of the fundamental mode: L=λ2⇒λ=2LL = \frac{\lambda}{2} \Rightarrow \lambda = 2L
The speed of sound vv relates to frequency ff and wavelength λ\lambda by the formula: v=fλv = f \lambda
Combining both equations: f=v2Lf = \frac{v}{2L}
Substituting the values:
- v=343 m/sv = 343 \, \text{m/s} (standard speed of sound at room temperature),
- L=64 ft=64×0.3048=19.51 mL = 64 \, \text{ft} = 64 \times 0.3048 = 19.51 \, \text{m}
f=3432×19.51≈8.8 Hzf = \frac{343}{2 \times 19.51} \approx 8.8 \, \text{Hz}
This very low frequency is in the infrasonic range—below the range of human hearing (which starts around 20 Hz)—but it can still be felt as vibration. Such pipes are used in large pipe organs to produce powerful bass notes, adding richness and grandeur to music in large auditoriums like the Boardwalk Hall. These ultra-low frequencies create not only aural but physical sensations in listeners, contributing to the awe-inspiring experience of large organ music.
