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tube with a cap on one end, but open at the other end, has a fundamental frequency of 133.9 Hz. The speed of sound is 343 m/5. If the cap is removed, what is the new fundamental frequency of the tube?

User Alex DG
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Final answer:

When a capped tube is changed to open at both ends, its fundamental frequency doubles, hence the new fundamental frequency of a tube with the previous closed-pipe fundamental frequency of 133.9 Hz will become approximately 267.8 Hz.

Step-by-step explanation:

If a tube with a cap on one end and open at the other has a fundamental frequency of 133.9 Hz, it is functioning as a closed-pipe resonator. When one end is capped, the tube resonates at its fundamental frequency with a quarter wavelength fitting inside the tube. However, if the cap is removed, the situation changes because both ends are open and the tube becomes an open-pipe resonator. For an open pipe, the fundamental frequency occurs when a half wavelength fits inside the tube. Therefore, the fundamental frequency will double as the tube now allows for a half wavelength to fit instead of a quarter of a wavelength. With the given fundamental frequency of a closed-pipe as 133.9 Hz, when the cap is removed, the new fundamental frequency of the tube would be approximately 267.8 Hz.

User Stephane Chazelas
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