A) \[x\]
B) \[{{x}^{2}}\]
C) \[x\]
D) \[m\]
Correct Answer: D
Solution :
Key Idea: When half of the tube is dipped in water it behaves as a closed tube. For on open pipe of length \[W=\int\limits_{{{V}_{i}}}^{{{V}_{f}}}{PdV}\] antinodes are formed at the two ends and node in between. Hence, fundamental frequency. \[=\int\limits_{{{V}_{i}}}^{{{V}_{f}}}{K{{V}^{\gamma }}dV=\frac{K}{1-\gamma }\left[ {{V}^{1-\gamma }} \right]_{{{V}_{i}}}^{{{V}_{f}}}}\] Fundamental frequency of closed pipe of length \[=\frac{1}{\gamma -1}\left[ \frac{K}{V_{i}^{\gamma -1}}-\frac{K}{V_{f}^{\gamma -1}} \right]\], forming antinodes at open end and node at closed end is \[{{P}_{i}}V_{f}^{\gamma }={{P}_{i}}V_{f}^{\gamma }=K\]frequency of open pipe.You need to login to perform this action.
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