Waves: Sound & Acoustics

• Formulate progressive mechanical wave functions: y = A sin(kx - ωt).
• Derive Newton's formula and Laplace's correction for sound speed in gases.
• Analyze standing waves, nodes, and antinodes in stretched strings and organ pipes.
• Calculate beat frequency and explain the Doppler effect for relative acoustic motion.

• Wave Velocity (v = νλ = ω/k)
• Laplace Sound Velocity: v = sqrt(γP/ρ)
• Superposition Principle & Interference
• Standing Waves in Strings (f_n = n v / 2L)
• Closed and Open Organ Pipe Harmonics
• Beats Frequency (f_b = |f1 - f2|)
• Doppler Effect Formula for Sound

“Closed pipes produce only odd harmonics (1, 3, 5...), whereas open pipes produce both odd and even harmonics.”

• •In standing waves, energy is trapped between nodes; no net energy transport occurs.
• •Laplace correction accounts for adiabatic compression during acoustic wave propagation.
• •Beat frequency equals the arithmetic difference between two source frequencies.

Practice sets on organ pipe resonance, sonometer tuning, and Doppler acoustic frequency shifts.