At 300 K three monatomic gases X, Y and Z have molar masses 4 g mol , 20 g mol and 40…
PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
At 300 K three monatomic gases X, Y and Z have molar masses 4 g mol−1, 20 g mol−1 and 40 g mol−1 respectively. The ratio of specific heats γ may be taken to be the same for all three.
(i) Show that for any two gases kept under identical conditions the ratio of their sound speeds is inversely proportional to the square root of the ratio of their molar masses.
(ii) Using the result in part (i), find the numerical ratio vX:vY:vZ of the speeds of sound in the three gases.
(iii) A musical note of 500 Hz is sent through each gas at 300 K. Identify the gas in which the wavelength of this note will be shortest and support your answer with calculation.