The speed of sound

The speed of sound is how far a crest travels each second. In one time period, the wave moves forward exactly one wavelength. So:

speed = wavelength ÷ time period, or v = λ/T = λν (wavelength × frequency).

Sound travels fastest in solids and slowest in gases:

Sound is about 4 to 5 times faster in water, and 15 to 20 times faster in solids, than in air.

Temperature and humidity change the speed in air. In dry air it is about 331 m s⁻¹ at 0 °C and nearly 344 m s⁻¹ at 22 °C: warmer air carries sound faster. Humid air carries it faster too.

"Does a louder or higher sound travel faster?" No. In air, the speed depends only on the medium, not on how loud the sound is or its frequency. Shouting louder changes the size of the wave, not its speed. If the frequency changes, the wavelength changes instead, so that λ × ν stays the same.

Lightning and thunder. You see the lightning first and hear the thunder later. Light travels at 300,000 km per second, so it reaches you almost at once; sound is far slower. So:

distance to the lightning ≈ speed of sound × the delay in seconds.

A 5-second delay means about 340 × 5 = 1700 m away. Count the seconds next time there's a storm.