34.1k views
1 vote
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
by
8.8k points

1 Answer

5 votes

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
by
8.4k points

No related questions found