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Obtain the equation of speed of sound wave in air and give the error in this equations. |
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Answer» Solution :Equationof 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. |
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