A pipe has a length of Im. Determine the frequencies of the fundamental and first two harmonic if the pipe is opened at both ends, (speed of sound in air = 340 m/s)
Correct answer: A. 170 Hz, 340 Hz, 510 Hz
- A. 170 Hz, 340 Hz, 510 Hz
- B. 120 Hz, 220 Hz, 390 Hz
- C. 90 Hz., 230 Hz, 440 Hz
- D. 210 Hz, 410 Hz, 510 Hz
Explanation
For a pipe opened at both ends, the fundamental frequency is given by F1 = v/2L. In this case, F1 = 340/2(1) = 170 Hz. The first harmonic (F2) is 2 times the fundamental frequency, so F2 = 2 × 170 = 340 Hz. The second harmonic (F3) is 3 times the fundamental frequency, so F3 = 3 × 170 = 510 Hz. Option A provides the correct frequencies based on these calculations, making it the right choice.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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