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 :
Let\[l=\]length of the pipe and\[d=\]diameter of the pipe In the fundamental mode of vibration \[\frac{\pi }{4}=(l+0.3d)\] where, 0.3 d is the necessary end correction. Frequency, \[n=\frac{v}{\lambda }=\frac{v}{4(l+0.3d)}\] As\[l\]is same wider pipe will resonate at a lower frequency, Le.,\[{{n}_{A}}<{{n}_{B}}\].
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