Question 407: Waves

Question

A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes

Accepted Answer

The fundamental frequency of open tube is
$$\mathrm{n}_1=\frac{\mathrm{v}}{2 \ell_1}$$
When tube is dipped in water, one-fourth of it is in water and three-fourth is in air. Hence, it becomes a tube closed at one end with length $$\ell_2=\frac{3}{4} \ell_1$$
The fundamental frequency of closed tube is
$$\begin{aligned}
\mathrm{n}_2 & =\frac{\mathrm{v}}{4 \ell_2} \
	herefore \quad \frac{\mathrm{n}_2}{\mathrm{n}_1} & =\frac{1}{4 \ell_2} 	imes 2 \ell_1=\frac{\ell_1}{2 \ell_2} \
& =\frac{4}{2 	imes 3} \quad\left[\because \frac{\ell_1}{\ell_2}=\frac{4}{3}ight] \
& =\frac{2}{3} \mathrm{n} \
	herefore \quad \mathrm{n}_2 & =\frac{2}{3} \mathrm{n}_1=\frac{2}{3} \mathrm{n}
\end{aligned}$$

Answer

$$\frac{3 n}{4}$$

Answer

$$\frac{n}{2}$$

Answer

$$n$$

Answer

$$\frac{2 n}{3}$$

Waves

A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes

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