Organs typically have several different sets of pipes tuned to the same pitches.

Question

Organs typically have several different sets of pipes tuned to the same pitches. The different sets of pipes, known as "stops," make different sounds. Imagine that an organ has a pipe in the Bourdon stop which is precisely tuned to middle C with a frequency of 261.63 Hz. But the middle C pipe in the Clarion stop produces a frequency which is a little low. When you play them together, you hear beating at 6.90 Hz. Assuming that the beating is due to the fundamental modes of the two pipes, that the Clarion pipe is open at both ends, and that the speed of sound is 343 m/s, what length of pipe do we need to cut off of the Clarion pipe to get it in tune? (Answer: _____mm (

Explanation / Answer

1) (a)
V= 43.2 mph = 19.31213 m/s
f (v+vauto / v-vauto) = 245.0Hz ((343 + 19.31213)/(343 - 19.31213)) = 274.23478 Hz

(b)

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