## Velocity of Sound Wave in Gas

**Newtons formula** is first derived by sir *lssac Newton*. Sound wave is a mechanical longitudinal that can propagate through through air medium in the form of alternate compression and rarefaction.

In the region of compression heat is evolved and heat is absorbed in the reason of refraction. So, heat developed in compression region can be easily transferred to the reason of rarefraction.As a result , the temperature of gas remain unchanged.

From this above fact, **Newtons** assume that the propagation of sound wave in air is **isothermal process**.then,the **velocity of sound in air** medium can be written as,

**V = √(K _{iso}/d) ……….1)**

* ,where K _{iso} = Isothermal bulk modules of elasticity of air*

** d = density of air**

The equation of state for **isothermal change** is,

**PV = constant ……….2)**

Differentiating equation 2 with respect to ‘T’

**d(PV)/dT = 0**

**or, PdV/dT + VdP/dT = 0**

**or, p = -dP/(dV/V)**

** or, P = -Stress/strain **

** or, P = K_{iso} ………….3)**

Negative sign inducates increase in pressure, decrease in volume and vice versa.

From equation 1 & 2, we get

** V = √(P/d)**

Hence, This is required exoression of **newton’s formula for velocity of sound wave in gas. **

**Questions**

1)State and prove Hall Effect?

2)State and prove Joule’s laws of heating?

3)What do you meant by Shunt? Describe its use in converting a Galvanometer into Ammeter?