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Question

In a long cylindrical tube, an air-column is constructed by fitting a movable piston. A tuning fork of frequency $$416Hz$$ sends longitudinal sound waves. Consider the speed of sound in the air as $$333m/s$$. It is observed that the air-column in the tube vibrates in its fundamental frequency. How far from the open end should the piston be in this situation?


A
10cm
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B
20cm
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C
30cm
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D
40cm
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Solution

The correct option is B $$20cm$$
At the piston end, pressure-antinode will be formed. At the open end, there will be a pressure node.

The length of the tube should be $$\dfrac{\lambda}{4}$$.

From, $$\lambda = \dfrac{Speed}{Frequency} = \dfrac{u}{\nu} = \dfrac{333}{416} = 0.8m$$

Length of the tube is:

$$L = \dfrac{\lambda}{4}$$

$$\Rightarrow L = \dfrac{0.8}{4} = 0.2m$$

$$= 20cm$$

2032355_1962843_ans_384cf170159243e3a6d24a7bd9fe1bc9.png

Physics

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