Properties of Wave Pulses and Waves

A wave transports energy between two locations while the medium stays put: each particle oscillates about its own equilibrium position and goes nowhere, so the cork bobs in place and the air molecule near a speaker moves back and forth about a fixed spot. A wave is transverse or longitudinal according to the direction a single particle moves relative to the direction of travel, which makes sound longitudinal however it is drawn. The speed of a mechanical wave is fixed by the medium, $v = \sqrt{F_T/(m/L)}$ on a string, so nothing the source does can change it.

Three errors dominate. Picturing the medium itself travelling with the wave, so air drifts across the room toward a listener. Calling a wave transverse because the drawing looks like a sine curve, without asking what the vertical axis plots or which way the particles actually move. And treating the wave speed as something the source controls, so shaking a rope harder or shouting louder is expected to speed the wave up, when those change the amplitude and the frequency and leave $v$ alone.