For the following questions, statement as well as the...

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$. (b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$. (c) Statement $-1$ is true, statement $-2$ is false (d) Statement $-1$ is false, statement $-2$ is true Statement $-1:$ Newton's equation for speed of sound was found wrong because he assumed the process to be isothermal. Statement $-2:$ When sound propagates, the compressions and rarefactions happen so rapidly that there is not enough time for heat to be distributed. (A) a (B) $b$ (C) $c$ (D) $\mathrm{d}$

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ Newton's equation for speed of sound was found wrong because he assumed the process to be isothermal. Statement $-2:$ When sound propagates, the compressions and rarefactions happen so rapidly that there is not enough time for heat to be distributed.
(A) a
(B) $b$
(C) $c$
(D) $\mathrm{d}$

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Key Concepts

Speed of Sound

The speed of sound is the rate at which small disturbances or pressure waves propagate through a medium. Its value depends on the medium’s compressibility and density, and the relationship between these properties is used to derive the speed in various conditions.

Isothermal and Adiabatic Processes

Isothermal processes maintain a constant temperature during the compression or expansion of a medium, while adiabatic processes occur without heat exchange, causing temperature changes. The derivation of the speed of sound is affected by whether the process is assumed to be isothermal or adiabatic, with adiabatic conditions generally providing a more accurate representation for rapidly propagating sound waves.

Heat Transfer Dynamics in Sound Propagation

In the context of sound propagation, the rapid compressions and rarefactions occur so quickly that there is little to no time for heat to be redistributed within the medium. This lack of heat exchange makes the process effectively adiabatic, which in turn influences the correct formulation for the speed of sound.

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