Newton was of the opinion that when longitudinal waves travel in gaseous medium, the changes taking place in the medium are isothermal in nature. Thus, according to Newton, the temperature of the gaseous medium remains constant, when sound travels through it. At the regions of compression, where the heat is produced, the heat is conducted away to the surrounding medium and at the regions of rarefaction, where cooling is produced, the heat is conducted in from the surrounding medium.
Thus Newton was of the idea that he had to consider the isothermal bulk modulus of gas in the equation of velocity, whose value is equal to the initial pressure.
Thus Newton was of the idea that he had to consider the isothermal bulk modulus of gas in the equation of velocity, whose value is equal to the initial pressure.
Laplace's correction
Laplace, in 1816, discovered the error in Newton’s formula and modified it satisfactorily. Laplace pointed out that it was wrong to assume that changes taking place in a gaseous medium are isothermal in nature, when sound waves travel through it.
Actually when sound waves travel in a gaseous medium then at any point in the medium the states of compression and rarefaction occur alternately. at the moment of compression, heat is produced and while at the moment of rarefaction, some cooling is produced. The compressions and rarefactions occur so quickly that heat produced during compression cannot go out into the surroundings, and the heat disappeared during rarefactions cannot come in from the surroundings. Moreover the exchange of heat does not occur because gases are bad conductors of heat. i.e, process of propagation of sound waves in gases is adiabatic in nature and the modulus in the formula should actually represent the adiabatic bulk modulus of gas whose value is equal to
times the initial pressure.
Actually when sound waves travel in a gaseous medium then at any point in the medium the states of compression and rarefaction occur alternately. at the moment of compression, heat is produced and while at the moment of rarefaction, some cooling is produced. The compressions and rarefactions occur so quickly that heat produced during compression cannot go out into the surroundings, and the heat disappeared during rarefactions cannot come in from the surroundings. Moreover the exchange of heat does not occur because gases are bad conductors of heat. i.e, process of propagation of sound waves in gases is adiabatic in nature and the modulus in the formula should actually represent the adiabatic bulk modulus of gas whose value is equal to
times the initial pressure.
No comments:
Post a Comment