Two wavelengths of sodium light $$590 \mathrm{~nm}$$ and $$596 \mathrm{~nm}$$ are used one after another to study diffraction due to single slit of aperture $$2 \times 10^{-6} \mathrm{~m}$$. The distance between the slit and the screen is $$1.5 \mathrm{~m}$$. The separation between the positions of first maximum of the diffraction pattern obtained in the two cases is

A coil having an inductance of $$\frac{1}{\pi} \mathrm{H}$$ is connected in series with a resistance of $$300 \Omega$$. If $$20 \mathrm{~V}$$ from a $$200 \mathrm{~Hz}$$ source are impressed across the combination, the value of the phase angle between the voltage and the current is

The pressure and density of a diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ changes adiabatically from $$(\mathrm{P}, \rho)$$ to $$\left(\mathrm{P}^{\prime}, \rho^{\prime}\right)$$. If $$\frac{\rho^{\prime}}{\rho}=32$$ then $$\frac{\mathrm{P}^{\prime}}{\mathrm{P}}$$ should be

A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the speed of sound. The ratio of apparent to real frequency is