Standing Wave in String and Organ Pipe: Practice Problem & Solution
The number of possible natural oscillations of air column in a pipe closed at one end of length $85 \text{ cm}$ whose frequencies lie below $1250 \text{ Hz}$ are (velocity of sound = $340 \text{ m s}^{-1}$): (2014)
Solution Explained:
To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:
Fundamental $f_0 = v / 4L = 340 / (4 \times 0.85) = 100 \text{ Hz}$. Frequencies are odd multiples: 100, 300, 500, 700, 900, 1100. All lie below 1250 Hz. Count is 6.
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