The speed of sound in a gas is v = √(γP/ρ). This is the
A{'text': 'Newton formula assuming isothermal propagation', 'label': 'A'}
B{'text': 'Doppler formula for observed frequency shifts', 'label': 'B'}
C{'text': 'Laplace-corrected Newton formula for adiabatic', 'label': 'C'}
D{'text': 'Bernoulli formula for fluid dynamics streamlines', 'label': 'D'}
Answer & Solution
Correct answer: C. {'text': 'Laplace-corrected Newton formula for adiabatic', 'label': 'C'}
1. Newton assumed sound propagates isothermally, giving v = √(P/ρ) — too low.
2. Laplace corrected: sound propagation is adiabatic, so v = √(γP/ρ).
3. γ = C_p / C_v is the ratio of specific heats.
4. This agrees with experimental values for air (v ≈ 340 m/s at STP).
_Source: NCERT Class 11 Physics, Ch 14 "Waves", §14.4_
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