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 $-1:$ When pressure in a gas changes, velocity of sound in gas may change. Statement $-2:$ Velocity of sound is directly proportional to square root of pressure. (A) a (B) $b$ (C) $\mathrm{c}$ (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 $-1:$ When pressure in a gas changes, velocity of sound in gas may change. Statement $-2:$ Velocity of sound is directly proportional to square root of pressure.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

Key Concepts

Statement and Reason Question Analysis

This type of question requires evaluation of both the truth of given statements and whether the reason provided logically and correctly explains the statement. Understanding the underlying physical principles, such as those governing sound propagation and gas behavior, is essential to determine the validity and connection of each statement.

Adiabatic Processes

Sound propagation in gases is often assumed to occur under adiabatic conditions, where no heat is transferred in or out during the rapid compressions and expansions of sound waves. This assumption leads to the pressure and density being related by the adiabatic relation (P ? ?^?), which is essential for deriving the speed of sound in a gas.

Speed of Sound in Gases

The speed of sound in a gas is determined primarily by the gas's temperature and specific heat properties rather than directly by its pressure. In an ideal gas, the speed of sound is given by the equation v = ?(?RT), where ? is the adiabatic index, R is the gas constant, and T is the temperature in Kelvin.

Ideal Gas Relationships

The Ideal Gas Law (P = ?RT) shows the relationship between pressure, density, and temperature. Because changes in pressure are typically accompanied by changes in density in a manner that offsets the effect of pressure alone, the speed of sound in a gas under ideal conditions remains largely independent of pressure when temperature is constant.

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