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Air column in two identical tubes is vibrating. Tube A has one end closed and tube B has both ends open. Neglecting end correction, the ratio of the fundamental frequency of air column in tube A to that in tube B is
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The correct answer is:
$1: 2$
The correct option is (C).
Consider the following diagram:
Velocity of a wave $v$ in a given medium is fixed, as $v=\lambda \mathrm{f}$, where $\lambda$ is the wavelength and $f$ is the frequency.
Therefore,
$f \propto \frac{1}{\lambda}$
The ratio of frequencies in case A and case B is given by,
$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{2}$
Consider the following diagram:
Velocity of a wave $v$ in a given medium is fixed, as $v=\lambda \mathrm{f}$, where $\lambda$ is the wavelength and $f$ is the frequency.
Therefore,
$f \propto \frac{1}{\lambda}$
The ratio of frequencies in case A and case B is given by,
$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{2}$
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