1.State Newton's formula for speed of sound in air and explain Laplace's correction $v = \sqrt{\frac{\gamma P}{\rho}}$.
Sol: Newton assumed isothermal compression ($v = \sqrt{P/\rho} \approx 280\text{ m/s}$). Laplace corrected that sound propagation is adiabatic ($B = \gamma P \implies v = \sqrt{\gamma P / \rho} \approx 332\text{ m/s}$).
2.State Principle of Superposition of Waves and define stationary (standing) waves.
Sol: Resultant displacement $y = y_1 + y_2$. Stationary waves are produced by superposition of two identical progressive waves travelling in opposite directions.
3.Derive the fundamental frequency and harmonics of an organ pipe open at both ends ($f_n = n \frac{v}{2L}$).
Sol: Open pipe has antinodes at both ends: $\lambda_1 = 2L \implies f_1 = \frac{v}{2L}$. All harmonics present ($f_n = n f_1$, $n = 1,2,3...$).
4.What are Beats? Derive beat frequency formula $f_{beat} = |f_1 - f_2|$.
Sol: Periodic variation in sound intensity when two sound waves of slightly different frequencies superpose: $y = 2A \cos\left(\frac{\omega_1-\omega_2}{2} t\right) \sin\left(\frac{\omega_1+\omega_2}{2} t\right) \implies f_{beat} = |f_1 - f_2|$.
