Question

A hollow pipe (such as an organ pipe open at both ends) is made to go into resonance at frequency X"open. One end of the pipe is now covered and the pipe is again made to go into resonance, this time at frequency X"closed. Both resonances are first harmonics (fundamentals). How do these two resonances compare?

1) They are the same.
2) X"closed = 1/2X"open
3) X"closed = 2X"open
4) X"closed = √2 X"open
5) X"closed = 3/2X"open

Answer 1

The resonant frequencies of a hollow pipe open at both ends and closed at one end are different. The resonant frequency of a closed pipe is twice the resonant frequency of an open pipe. Therefore, X"closed = 2X"open.

Step-by-step explanation:

When a hollow pipe is open at both ends, it can go into resonance at a specific frequency called X″open. When one end of the pipe is covered, the pipe will go into resonance at a different frequency called X″closed. Both of these resonances are first harmonics or fundamentals. The relationship between X″open and X″closed for a pipe open at both ends and closed at one end is that X″closed = 2X″open. Therefore, option 3) X″closed = 2X″open is the correct answer.