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Question
Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340 ms−1.
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Solution
Given:
Speed of sound in air v = 340 m/s
Length of open organ pipe L = 20 cm = 20 × 10−2 m
Fundamental frequency \[\left( f \right)\] of an open organ pipe :
\[f = \left( \frac{v}{2L} \right) = \frac{340}{2 \times 20 \times {10}^{- 2}}=850\text { Hz }\]
First overtone frequency \[\left( f_1 \right)\] :
f1 = \[2f\]
\[\Rightarrow f_1 = \left( \frac{2V}{2I} \right) = 2 \times 850 = 1700 \text{ Hz }\]
Second overtone frequency \[\left( f_2 \right)\] :
\[f_2 = 3f\]\[ \Rightarrow f_2 = 3\left( \frac{V}{2L} \right) = 3 \times 850 = 2550 \text { Hz }\]
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