Q141 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Physics
A cylindrical tube open at both ends has a fundamental
frequency 'f' in air. The tube is dipped vertically in water so
that half of it is in water. The new fundamental frequency is
- Correct answerAf
- B$\frac{f}{2}$
- C2f
- D4f
Solution
Initially
$$
\mathrm{f}=\frac{\mathrm{V}}{2 \ell}
$$
Finally
From diagram, we can see $$ \begin{aligned} & \frac{\lambda}{4}=\frac{\ell}{2} \\ & \Rightarrow \lambda=21 \end{aligned} $$ Now, fundamental frequency $$ =\frac{\mathrm{V}}{\lambda}=\frac{\mathrm{V}}{2 \ell}=\mathrm{f} $$ So, there will be no change in fundamental frequency.
From diagram, we can see $$ \begin{aligned} & \frac{\lambda}{4}=\frac{\ell}{2} \\ & \Rightarrow \lambda=21 \end{aligned} $$ Now, fundamental frequency $$ =\frac{\mathrm{V}}{\lambda}=\frac{\mathrm{V}}{2 \ell}=\mathrm{f} $$ So, there will be no change in fundamental frequency.
Hence, the correct answer is option: 'A'.