Q.The Laplace's correction in the expression for velocity of sound given by Newton is needed because sound waves (A) are longitudinal (B) propagate isothermally (C) propagate adiabatically (D) are of long wavelength

[!TLDR] Laplace corrected Newton's formula because sound's compressions/rarefactions happen too fast for heat to escape, making the process adiabat …

Newton's original formula, $v=\sqrt{P/\rho}$, assumed sound propagation in air is an ISOTHERMAL process (constant temperature), using the isothermal bulk modulus (=P for a gas); this predicted $v\approx279.9$ m/s at NTP, about 16% below the experimental ~332 m/s. Laplace recognised that a sound wave's compressions and rarefactions happen far too rapidly (hundreds of times per second, for audible frequencies) for the heat generated during compression to actually dissipate away before the next rarefaction -- so the true process is ADIABATIC (no net heat transfer), and the correct modulus to use is the adiabatic modulus $E=\gamma P$, giving the corrected formula $v=\sqrt{\gamma P/\rho}\approx332.3$ m/s, matching experiment. So the correction is needed specifically because sound actuall …

Recall that Laplace's correction replaces Newton's isothermal assumption with the adiabatic one, because the compression/rarefaction cycle o …

Mixing up the direction of the correction -- some students recall 'isothermal vs adiabatic' but then pick (B) 'propagate isothermally' as the answer, forgetting that isothermal was Newton's WRONG assu …