In the propagation of longitudinal waves in a fluid contained in an infinitely long tube of cross-section $A$, show that $$ \rho=\rho_o\left(1-\frac{\partial \xi}{\partial x}\right) $$ where, $\rho_0=$ equilibrium density $\rho=$ density of the fluid in the disturbed state $$ \frac{\partial \xi}{\partial x}=\text { volume strain }\left(\left|\frac{\partial \xi}{\partial x}\right| \ll 1\right) $$ [TC][15 Marks] [2010]
Write down the one-dimensional harmonic oscillator differential equation under damping and its solution for the lightly damped condition, with the meanings of symbols. Determine the dependent energy in the lightly damped condition. [TC][10 Marks][2011]
Explain the physical significance of group velocity from the concept of phase velocity with relevant expressions. [TC][15 Marks][2011]
Prove that the group velocity $V_g$ of electromagnetic waves in a dispersive medium with refractive index $n\left(\lambda_0\right)$ at wavelength $\lambda_0$ is given by $$ V_g=\frac{c}{n\left(\lambda_0\right)-\lambda_0 \frac{d n\left(\lambda_0\right)}{d \lambda_0}} $$ where $c$ is the free space velocity of light. Find the time taken for the electromagnetic pulse to travel a distance $D$. [TC][20 Marks][2011]
Waves and Optics PYQ 2010-2023
Consolidated PYQ of Waves and Optics 2010-2023
September 24, 2023