Ion acoustic waves are a type of electrostatic wave that propagates through a plasma consisting of ions and electrons. They are generated due to the temperature and density fluctuations in the plasma, which give rise to pressure gradients that drive the oscillations.

The wave speed of ion acoustic waves is determined by the ion temperature, and their wavelength is determined by the plasma density. These waves play an important role in a variety of plasma phenomena, such as plasma heating and confinement in fusion devices, the propagation of solar wind, and the formation of structures in the Earth's ionosphere.

In addition, ion acoustic waves are studied in the field of plasma physics as they provide a means to understand the collective behaviour of charged particles in plasmas. They are also used as a diagnostic tool to measure the plasma properties in laboratory experiments and in space.

The motion of massive ion will produce very low frequency so we consider

ni = ne = n

The ion fluid equation in the absence of magnetic field is

By linearization method we assume

Since, the oscillating quantities are assumed to behave sinusoidal as

We assume that the ion follows Boltzmann distribution as

Now, equation of continuity is given as

which is the required dispersion relation for ion acoustic wave.

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