Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $$10.2 \mathrm{~V}$$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $$=1245 \mathrm{~eV} \mathrm{~nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$).

A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and length $$2 \mathrm{~m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \mathrm{~kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta=\frac{1}{100}$$ radian on the points of support. The value of A is ________ $$\times 10^{-4} \mathrm{~m}^2$$ (consider $$x<<\mathrm{L}$$ ).

(given : $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)