How do vibrations cause sound waves

 sound waves are a type of wave sometimes called compression waves, vibrations with enough of an amplitude can compress and decompress the air adjacent to the object causing the waves to form.

Sound consists of compression waves in some material—usually air. Sound wavesare created by the vibration of some object or even air itself. They can be created by a back-and-forth motion of an object, by having air pass over a vibrating object, or by moving air causing the vibrations.

Wavelength divides in half and speed stays the same.