Question

The speed of sound in a fluid is the velocity at which a weak pressure wave propagates in the medium.

• A. Isothermally
• B. Adiabatically
• C. Isobarically
• D. Isentropically

Hint:

Remember the Laplace correction for the speed of sound. Newton assumed the process was isothermal, but Laplace correctly argued it was too fast for heat transfer, making it adiabatic. For an ideal fluid with a weak wave, this adiabatic process is also reversible, hence isentropic. If both "Adiabatically" and "Isentropically" are options, "Isentropically" is the more precise answer.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks about the thermodynamic nature of the process of sound propagation in a fluid. Sound waves are mechanical waves that travel as a series of compressions and rarefactions.
Step 2: Detailed Explanation:


The compressions and rarefactions of a sound wave occur very rapidly. This rapid nature means there is insufficient time for significant heat exchange to occur between the compressed (slightly hotter) regions and the rarefied (slightly cooler) regions. A process with negligible heat transfer is defined as adiabatic. This eliminates option (A) Isothermally, which was Newton's incorrect initial assumption.
Option (C) Isobarically is incorrect by definition, as a sound wave is fundamentally a pressure wave, meaning pressure varies.
The question specifies a "weak pressure wave". In this context, "weak" implies that the process is nearly reversible, with minimal energy dissipation due to effects like viscosity or thermal conduction.
A process that is both reversible and adiabatic is defined as isentropic (constant entropy).
While the process is adiabatic (Option B), the term isentropic (Option D) is more precise and complete because it also implies reversibility, which is a key assumption in the standard derivation for the speed of sound.

Step 3: Final Answer:
Given the options, "Isentropically" is the most accurate and specific description of the propagation of a weak sound wave.