What happens to the speed of a longitudinal wave in a gas if the pressure is increased while temperature remains constan
**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. For an ideal gas, v = √((gamma P/rho)) , and P/rho = RT/M (constant at constant temperature). Thus, speed depends only on temperature and gamma , not pressure alone, so it remains unchanged. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Remain
Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves
