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
B
20cm
C
30cm
D
40cm

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:$$L = \dfrac{\lambda}{4}$$$$\Rightarrow L = \dfrac{0.8}{4} = 0.2m$$$$= 20cm$$Physics

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