Question

The fundamental frequency of an air column in a pipe closed at one end is 150 Hz. If the same pipe is open at both ends, the frequencies produced in Hz are

• A. 150, 300, 450, 600, ...
• B. 300, 450, 600, 750, ...
• C. 300, 400, 500, 600, ...
• D. 300, 600, 900, 1200, ...

Hint:

Open pipe fundamental is twice that of a closed pipe of the same length.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The frequency of a pipe depends on whether it is open at one end or both ends. We calculate the new fundamental and its harmonics.

Step 2: Key Formula or Approach:
1. Closed pipe fundamental: \( f_c = \frac{v}{4L} = 150 \).
2. Open pipe fundamental: \( f_o = \frac{v}{2L} \).
3. Harmonics: Open pipes produce all integer multiples (\( n f_o \)).

Step 3: Detailed Explanation:
From the closed pipe data: \( \frac{v}{4L} = 150 \implies \frac{v}{2L} = 300 \).
So, for an open pipe of the same length, the fundamental frequency is 300 Hz.
An open pipe produces all harmonics: 1st, 2nd, 3rd...
Frequencies \( = 1 \times 300, 2 \times 300, 3 \times 300 \dots \)
Frequencies \( = 300, 600, 900, 1200 \dots \)

Step 4: Final Answer:
The frequencies are \( 300, 600, 900, 1200 \dots \).