A pipe of length L is closed at one end. Another pipe is open at both ends and has length 2L.What is the lowest common frequency for the standing waves in the pipes?
Question
A pipe of length L is closed at one end. Another pipe is open at both ends and has length 2L.What is the lowest common frequency for the standing waves in the pipes?
Solution
The fundamental frequency (or first harmonic) for a pipe closed at one end (1st pipe) and open at both ends (2nd pipe) is given by the formula:
f = v / 4L for the 1st pipe (closed at one end) f = v / 2L for the 2nd pipe (open at both ends)
where:
- f is the frequency,
- v is the speed of sound, and
- L is the length of the pipe.
Given that the 2nd pipe is twice as long as the 1st pipe (2L), the fundamental frequency for the 2nd pipe becomes:
f = v / 2(2L) = v / 4L
So, the fundamental frequency for both pipes is the same, which means the lowest common frequency for the standing waves in the pipes is v / 4L.
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