Q.At what temperature will the speed of sound in air be 1.75 times its speed at N.T.P?

Three environmental factors change the measured speed of sound in air. Pressure alone, at constant temperature, has NO effect: since $v=\sqrt{\gamma P/\rho}=\sqrt{\gamma PV/M}$, and Boyle's Law fixes $PV$ constant at constant temperature (with M and γ themselves constant), v stays unchanged -- a pressure change matters only if it comes with a temperature change.

Temperature raises the speed of sound: since $v\propto\sqrt{T}$ (absolute temperature), $v/v_0=\sqrt{T/T_0}$, and for modest temperature changes this simplifies (via a binomial approximation around $T_0=273$ K) to $v\approx v_0+0.61t$ for a Celsius temperature t -- about a 0.61 m/s increase in speed for every 1°C rise. …