Air column in two identical tubes is vibrating. Tube A has one end closed and tube B has both ends open.…

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
  1. $1: 4$
  2. $4: 1$
  3. $1: 2$
  4. $2: 2$

Solution

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, $\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{2}$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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