State Newton's formula for speed of sound in a gas. Discuse the Laplace correction
Answers
Explanation:
Newton’s Calculation: The velocity of sound that propagates in a gas medium was first formulated by Newton.
He stated the formula of the velocity of the propagation of sound in a gas medium by assuming that the sound wave going through the gas medium in the isothermal process.
In the time of propagation of the sound, the pressure and the volume of many parts of the gas medium can be changed due to the compression and rarefaction but the temperature of the medium remains constant.
Let us consider, for a part of the gas a certain amount of pressure is PP and volume is VV. During the propagation of the sound, the pressure becomes (P+P1)(P+P1) by increasing and hence the volume becomes (V−v)(V−v) by decreasing.
Since the temperature is constant, from Boyle's law,
PV=(P+P1)(V−v)PV=(P+P1)(V−v)
On multiplying the term and we get,
⇒PV=PV+P1V−Pv−P1v⇒PV=PV+P1V−Pv−P1v
⇒0=P1V−Pv⇒0=P1V−Pv [The term P1vP1v is too small and hence neglected]
⇒Pv=P1V⇒Pv=P1V
⇒P1Vv=P⇒P1Vv=P
On rewriting the terms and we get,
⇒P=P1vV=volume stressvolume strain⇒P=P1vV=volume stressvolume strain
bulk modulus = k=volume stressvolume strainbulk modulus = k=volume stressvolume strain
∴P=k