Sound waves travel slower in colder air than in warmer air why does the speed of sound depend on air temperature?

When air is warmer, the air particles move faster due to the heat, causing kinetic energy of the particles to increase. And as sound is produced when energy is transfered from one particle to another, with the particles moving faster, the energy will also be transfered faster, thus, allowing sound waves to travel faster in warmer air than in colder air