The change in pressure and volume of air when a sound wave passes through it is an example of an adiabatic process.

Explanation:

The term "adiabatic" refers to a process in which no heat is exchanged between the system and its surroundings. In the case of a sound wave passing through air, the process is adiabatic because there is no transfer of heat between the air and its surroundings.

When a sound wave travels through air, it causes compression and rarefaction of the air molecules. These changes in pressure and volume occur due to the vibrations of the sound source. Let's understand the changes in pressure and volume during this process:

1. Compression: As the sound wave propagates through the air, it causes regions of high pressure called compressions. In a compression, the air molecules are pushed closer together, resulting in an increase in pressure.

2. Rarefaction: Along with compressions, sound waves also create regions of low pressure called rarefactions. In a rarefaction, the air molecules spread apart, leading to a decrease in pressure.

During these compressions and rarefactions, the volume of the air also changes. When the air molecules are compressed, the volume decreases, and when they undergo rarefaction, the volume increases.

Now, let's see why this process is considered adiabatic:

- No heat transfer: The changes in pressure and volume during the passage of a sound wave are due to the mechanical vibrations of the sound source. There is no transfer of heat between the air and its surroundings during this process. Therefore, the process is adiabatic.

- Conservation of energy: The changes in pressure and volume are accompanied by the conservation of energy in the system. The energy of the sound wave is converted into changes in pressure and volume, without any heat exchange.

In conclusion, the change in pressure and volume of air when a sound wave passes through it is an adiabatic process because there is no heat transfer involved. The compressions and rarefactions caused by the sound wave lead to changes in pressure and volume, which are purely mechanical in nature.

Since isothermal process follows Boyle, s law... Pv=const. Therefore answer is (A)