12_InstSolManual_PDF_Part9

12_InstSolManual_PDF_Part9 - Mechanical Waves and Sound...

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(b) (c) 12.31. Set Up: For an open pipe the first overtone has frequency For a stopped pipe the first overtone has frequency The mouthpiece acts as a closed end. Solve: (a) (b) A pipe closed at both ends has the same overtone frequencies as a pipe open at both ends (Problem 12.28). Reflect: The fundamental frequency for a stopped pipe is lower by a factor of two than the fundamental frequency for a pipe of the same length but closed at both ends. But for the stopped pipe the first overtone is the third harmonic and the first overtone is lower than that of the other pipe only by a factor of 12.32. Set Up: For a stopped pipe only odd harmonics are present. Solve: (a) If it is an open pipe, and This says and n must be an integer, so the pipe is not an open pipe. If it is a stopped pipe, and This says and The pipe is stopped. (b) These are the and harmonics. (c) and 12.33. Set Up: The path difference for the two sources is d . For destructive interference, the path difference is a half-integer number of wavelengths. For constructive interference, the path difference is an integer number of
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