How do we derive that sound travels at a speed of 344 m/s ?

Derivation is not the only way to know that speed of sound is 344 m/s in air.

It's measured in experiments.

Also it can be calculated from, V = (C/ρ) where C is the bulk modulus of air and ρ is the density.

Even to use this formula we have to find the bulk modulus. Which can be derived for ideal gas or experimentally measured.

Regards,

Team,

TopperLearning.