Velocity of sound in air at pressure $$P$$ and temperature $$T$$ is $$V$$. Find the velocity of sound in air if it's (i) pressure alone is doubled (ii) Temperature alone is doubled (iii) pressure and temperature are both doubled

PLACEHOLDER ANSWER - the question has three answers. $$v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\gamma RT}{M}}$$, so the speed depends on temperature but not on pressure alone, since $$\frac{P}{\rho}$$ stays constant at fixed $$T$$. (i) It stays $$V$$. (ii) It becomes $$\sqrt{2}\,V$$. (iii) It becomes $$\sqrt{2}\,V$$.