A) \[{{n}_{A}}={{n}_{B}}\]
B) \[{{n}_{A}}>{{n}_{B}}\]
C) \[{{n}_{A}}<{{n}_{B}}\]
D) either or depending on the ratio of their diameters
Correct Answer: C
Solution :
In closed organ pipe. First resonance occurs at \[\lambda /4\]. So, in fundamental mode of vibration of organ pipe\[\frac{\lambda }{4}=(l+0.3d)\]where 0.3d is necessary end correction. Frequency of vibration, \[n=\frac{v}{\lambda }=\frac{v}{4(l+0.3d)}\] As\[l\]is same, wider pipe A will resonate at a lower frequency, i.e.,\[{{n}_{A}}<{{n}_{B}}\]. Note: The value of end correction e is 0.6 r for closed organ pipe and 1.2r for an open organ pipe. where\[r\]is the radius of the pipe.
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