A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = s_m cos (kx − ωt). Its velocity can be obtained from A) ω/k B) k/ω C) k D) ω E) ωk

Question

Quizplus · Accepted Answer

The velocity of a longitudinal wave in a compressible gas is given by v = √(γP/ρ), where γ is the adiabatic index, P is the pressure, and ρ is the density of the gas.

For a harmonic longitudinal wave, we have k = 2π/λ = ω/v, where λ is the wavelength and ω is the angular frequency.

Thus, v = ω/k = ω/(2π/λ) = λω/(2π) = ω/k.

Therefore, the best choice is A.

A Harmonic Longitudinal Wave Propagating Down a Tube Filled with a Compressible