For a gas having γ = 7/5, define vₗ as the sound speed predicted after Laplace's correction and vₙ as Newton's isothermal prediction. If (vₗ/vₙ)² = N/5, find N.
Physics · Wave Motion · sound wave
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Question

For a gas having γ = 7/5, define vₗ as the sound speed predicted after Laplace's correction and vₙ as Newton's isothermal prediction. If (vₗ/vₙ)² = N/5, find N.

G1 Physics · Accepted Answer

Newton's value is vₙ = √(P/ρ). Laplace's corrected value is vₗ = √(γP/ρ). Therefore, vₗ/vₙ = √γ. Squaring, (vₗ/vₙ)² = γ = 7/5. Hence, N = 7.