Repeat Prob. 7–57, except let speed of sound c in an ideal gas be a function only of pressure P and gas density ρ. Showing all your work, use dimensional analysis to find the functional relationship between these parameters. Verify that your results are consistent with the equation for speed of sound in an ideal gas,

Data from Problem 57

The speed of sound c in an ideal gas is known to be a function of the ratio of specific heats k, absolute temperature T, and specific ideal gas constant R_gas (Fig. P7–57). Showing all your work, use dimensional analysis to find the functional relationship between these parameters.

Fig. P7–57

Transcribed Image Text:

c = VKRT. gas