Q.3) A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :
A) $2 f$
B) $\frac{f}{2}$
C) $f$
D) $\frac{3 f}{2}$
Solution:
Initially, the pipe is open at both ends, so it supports a fundamental frequency $f$ with wavelength $\lambda=2 \mathrm{~L}$. When half is submerged, it behaves like a pipe open at one end (and closed at the other), now with effective length $\mathrm{L} / 2$. For such a pipe, the new fundamental frequency becomes $\mathrm{v} /(4 \times \mathrm{L} / 2)=\mathrm{v} /(2 \mathrm{~L})$, which is $3 \mathrm{f} / 2$ when compared with the original.