The frequency of stationary waves in an organ pipe for third overtone when both ends are open is given by:
Correct answer: D. f4 = 4v/(2L)
- A. f4 = v/2L
- B. f4 = 4/2L
- C. f4 = 3v/(2L)
- D. f4 = 4v/(2L)
Explanation
In an open organ pipe, the harmonics are integer multiples of the fundamental frequency. The nth harmonic frequency is given by fn = n(v/2L), where v is the speed of sound and L is the length of the pipe. The third overtone corresponds to the fourth harmonic (n = 4), so the frequency is f4 = 4(v/2L). This is why the correct answer is Option D.Option A represents the formula for the fundamental frequency, which is the first harmonic, not the third overtone. Option B is incorrect as it lacks the speed of sound 'v' in the formula. Option C is the formula for the second harmonic, not the third overtone.
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About Waves
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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