A tube open from the both the ends contains two arms, arm-1 and arm-2 and horizontal base, all of same length $l = 1 m$ each, and same small cross-section area. Water $(ρ_{w})$ and an unknown liquid of density $ρ$ is filled in U-tube initially U-tube is accelerating in horizontal direction at $a = \frac{g}{4} m / s^{2}$ . A tuning fork of frequency 300 Hz is vibrated on arm-1, then a loud sound of first overtone is produced. If same tuning fork is vibrated on arm-2, again a loud sound of fundamental tone is produced. Neglect surface tension and end correction liquids are immiscible for above explained state of motion length of two liquid in horizontal limb is 50cm for each.
Take : $V_{s o u n d} = 300 m / s$ , density of water $ρ_{w} = 10^{3} k g m^{- 3}, P_{a t m} = 10^{5} N m^{- 2}$

Question

Infinity Learn · Accepted Answer

Density of unknown liquid is $\frac{ρ_{w}}{7}$

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Horizontal acceleration of tube for which liquid in both arm resonates with same tuning fork is 1.2g (in same harmonic)

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Horizontal acceleration of tube for which liquid in both arm resonates with same tuning fork is g

Detailed Solution