Sound waves in air at standard atmospheric conditions propagate as longitudinal pressure disturbances.
(i) State the expression for the speed of sound in a gas as given originally by Newton and specify the thermodynamic condition implicit in his assumption.
(ii) At room temperature the experimentally measured value of the speed of sound in air is about 332ms−1, whereas Newton’s expression gives only about 280ms−1. Explain qualitatively the main physical reason for this discrepancy.
(iii) Laplace introduced a correction to Newton’s formula. Explain how this correction removes the error and briefly describe the role played by the ratio of specific heats γ in the corrected expression.