Question 424: Waves

Question

A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency $$500 \mathrm{~Hz}$$ is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$]

Accepted Answer

$$\begin{aligned}
& \mathrm{f}=500 \mathrm{~Hz}, \mathrm{v}=320 \mathrm{~m} / \mathrm{s} \
& \lambda=\frac{\mathrm{v}}{\mathrm{f}}=\frac{320}{500}=0.64 \mathrm{~cm}
\end{aligned}$$
Resonances will be obtained at air columns of lengths
$$\begin{aligned}
& \frac{\lambda}{4}, \frac{3 \lambda}{4}, \frac{5 \lambda}{4}, \frac{7 \lambda}{4}, \ldots . . \
& \frac{\lambda}{4}=\frac{64}{4}=16 \mathrm{~cm}
\end{aligned}$$
$$	herefore$$ Resonance can be obtained at $$16 \mathrm{~cm}, 48 \mathrm{~cm}, 80 \mathrm{~cm}, 105 \mathrm{~cm}, \ldots$$. Since the length of the tube is $$100 \mathrm{~cm}$$, only first three resonances can be obtained.

Answer

3

Answer

4

Answer

1

Answer

2

Waves

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