A stationary wave is set up in a pipe of length L. If the pipe is open at one end and closed at other, what is the ratio of the fifth harmonic frequency to the first harmonic frequency?
Correct answer: D. 5
- A. 4
- B. 6
- C. 1/5
- D. 5
Explanation
The frequency of the nth harmonic of a stationary wave in a pipe of length L open at one end and closed at the other is given by: fn = n(v/2L)where v is the speed of sound. For the first harmonic, n=1, so:f1 = (v/2L)For the fifth harmonic, n=5, so:f5 = 5(v/2L)The ratio of the fifth harmonic frequency to the first harmonic frequency is:f5/f1 = (5(v/2L))/(v/2L) = 5Therefore, the ratio of the fifth harmonic frequency to the first harmonic frequency is 5:1.Mathematically the other options are incorrect.
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About Organ Pipes
Organ pipes produce standing sound waves in air columns, with resonance determined by whether each end is open or closed. The topic covers nodes, antinodes, fundamental frequency, harmonics, wavelength and end correction. Open pipes support all harmonics, while closed pipes support only odd harmonics under the ideal model.
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