Question

A pipe open at both ends has length 1 m. The air column in the pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air = 340 m/s)

• A. 510 Hz
• B. 85 Hz
• C. 170 Hz
• D. 340 Hz

Hint:

An open pipe supports all harmonics starting from the fundamental frequency.

Answer 1

The Correct Option is B

Step 1: Formula for resonant frequencies of an open pipe.
For an open pipe:
\[ f_n = \frac{n v}{2L}, \quad n = 1,2,3,\dots \]

Step 2: Calculate fundamental frequency.
\[ f_1 = \frac{340}{2 \times 1} = 170 \, \text{Hz} \]

Step 3: Possible resonant frequencies.
\[ 170, 340, 510, \dots \]

Step 4: Identify non-resonant frequency.
85 Hz is not an integral multiple of 170 Hz.

Step 5: Conclusion.
The pipe cannot resonate at 85 Hz.