Question

In a resonance column experiment radius of column tube is 2cm and the frequency of tuning fork is 512 Hz.if zero of meter scale coincide with the top end of resonance column then reading of position of water column at resonance (speed of sound=340m/s) nearly...
1) 18.3 cm. 2) 15.4 cm. 3) 30cm. 4) 16.6cm

Answer 1

Answer on Question #51586-Physics-Mechanics-Kinematics-Dynamics

In a resonance column experiment radius of column tube is $r = 2cm$ and the frequency of tuning fork is $f = 512\,Hz$. if zero of meter scale coincide with the top end of resonance column then reading of position of water column at resonance (speed of sound $c = 340\frac{m}{s}$) nearly...

1) 18.3 cm. 2) 15.4 cm. 3) 30cm. 4) 16.6cm

Solution

End correction

$$e = 0.3d = 0.6r = 0.6 \cdot 2cm = 1.2\,cm.$$

Wavelength

$$\lambda = \frac{c}{f} = \frac{340\frac{m}{s}}{512\,Hz} = 0.664\,m = 66.4\,cm.$$

When the first resonance occurs,

$$L + e = \frac{\lambda}{4} \rightarrow L = \frac{\lambda}{4} - e = \frac{66.4\,cm}{4} - 1.2\,cm = 15.4\,cm.$$

Answer: 2) 15.4 cm.

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