A) \[~824\text{ }Hz,\text{ }1648\text{ }Hz\]
B) \[~412\text{ }Hz,\text{ }824\text{ }Hz\]
C) \[~206\text{ }Hz,\text{ }412\text{ }Hz\]
D) \[216\text{ }Hz,\text{ }824\text{ }Hz\]
Correct Answer: A
Solution :
Key Idea: When the dosed pipe is cut one open and one closed pipe are formed. When pipe is closed at one end \[n=\frac{v}{4l}\] Given, \[n=412\,Hz\] \[412=\frac{v}{4l}\] ?(i) When pipe is cut into two equal halves then length of each is \[\frac{l}{2}.\] \[{{n}_{1}}=\frac{v}{4l}\] (closed pipe) \[{{n}_{2}}=\frac{v}{2l}\] (open pipe) Where \[l=\frac{l}{2}\] \[{{n}_{1}}=\frac{v}{4\left( \frac{l}{2} \right)}\] Putting \[v=1648l\]from Eq. (i), we get \[{{n}_{1}}=\frac{1648l}{2l}=824\,Hz\] \[{{n}_{2}}=\frac{v}{2\left( \frac{l}{2} \right)}=\frac{v}{l}\,=\frac{1648\,l}{l}\,=1648\,Hz\] Note: A closed pipe produces only odd harmonics while an open pipe produces both even and odd harmonics.You need to login to perform this action.
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