A) \[f\propto \frac{1}{LD}\]
B) \[f\propto \frac{1}{L\sqrt{D}}\]
C) \[f\propto \frac{1}{{{D}^{2}}}\]
D) \[f\propto \frac{1}{L{{D}^{2}}}\]
Correct Answer: A
Solution :
The fundamental frequency is \[f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}\] \[f=\frac{1}{2L}\sqrt{\frac{T}{\rho \pi \frac{{{D}^{2}}}{4}}}=\frac{1}{LD}\sqrt{\frac{T}{\pi \rho }}\] \[\therefore \] \[f\propto \frac{1}{LD}\]
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