Obtain the equation of speed of sound wave in air and give the error in this equations.

Explanation

Equation of sound in gas (air),
`v = sqrt ((B)/(rho)) " "…(1)`
Newton suggested that the propagation of sound is an isothermal process.
`In PV = Nk _(B)T, N k _(B) T=` constant,
`therefore PV=` constnat `" "…(2)`
For an isothermal change in equation (2),
`VDelta P +PDelta V=0`
`therefore (Delta P)/(Delta V//P) = P`
`therefore B =P`
`therefore B = (-Delta P )/(Delta V//V)`
Therefore, from equation (1) the speed of a ongitudina wave in an ideal gas is given by, ` v = sqrt ((P)/(rho))`
It is known as Newton.s formula.
`v = sqrt ((P )/(rho )) = sqrt ((1.01 xx 10 ^(5))/( 1.29))`
`therefore v ~~ 280 ms ^(-1)`
Thus, value of speed of sound is `280 ms ^(-1)` according to Newton.s formula but its experimental value is `331 ms ^(-1).` Hence, value from Newton.s formula is `15%` less. So, assumption of Newton is not correct.