For a certain organ pipe, three successive resonance frequencies are observed at 425, 595, and 765 Hz. The speed of the sound in air is 340 m/s. The pipe is:
Correct answer: A. Closed pipe of length 1 m
- A. Closed pipe of length 1 m
- B. Closed pipe of length 2 m
- C. Open pipe of length 1 m
- D. Open pipe of length 2 m
Explanation
To find out which organ pipe is used, first, we will take the ratio of 3 observed harmonics: 425:595:765 5x 85 : 7x 85 : 9x 85 Since each successive harmonic is an odd number; the organ pipe is most likely a closed one and 85Hz is common for all so it is the fundamental frequency or f=425/5 = 85Hz f=595/7 =85Hz f=765/9= 85Hz Now: For fundamental frequency: L =v/4f = 340/85x4 = 1m answer!
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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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