Standing Wave in String and Organ Pipe: Practice Problem & Solution
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \text{ cm}$, the length of the open organ pipe is: (2018)
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 of open = $v / 2L_o$. Third harmonic of closed = $3v / 4L_c$. Equating them: $v / 2L_o = 3v / 4L_c \Rightarrow L_o = 2L_c / 3 = 2(20)/3 = 13.33 \text{ cm} \approx 13.2 \text{ cm}$.
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