Question

The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end are $n_1$ and $n_2$ respectively, then \dots

• A. $n_1 = n_2$
• B. $n_1 = 2n_2$
• C. $2n_1 = n_2$
• D. $3n_1 = 4n_2$

Hint:

Closing one end of a previously open tube immediately drops its fundamental pitch by exactly one full octave (halving its frequency). This is why instruments like the clarinet (effectively closed) can play much lower notes than flutes of similar size!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The fundamental frequency of an air column depends on whether the ends are open (antinodes) or closed (nodes).

Step 2: Formula Application:
For an open pipe of length $L$: $n_1 = V/2L$. For a closed pipe of length $L$: $n_2 = V/4L$.

Step 3: Explanation:
Comparing the two: $n_1 = \frac{V}{2L} = 2 \times \left( \frac{V}{4L} \right) = 2n_2$.

Step 4: Final Answer:
The relationship is $n_1 = 2n_2$.