Imagine a crowd doing "the wave" at a stadium. Each person only moves up and down — they do not travel around the stadium. Yet a pattern travels around the ring. That is the essence of wave motion: energy moves, matter stays.

Now imagine pushing one end of a slinky back and forth. The coils alternately bunch up (compression) and spread out (rarefaction). This is a longitudinal wave — the coils move in the same direction the compression travels. Sound in air is exactly this: air molecules jostle their neighbours and sit back; the disturbance propagates.

SHM is even simpler. Hang a mass on a spring. Pull it down a little and release. The spring force always pushes it back toward the middle: the bigger the displacement, the stronger the push. That restoring force proportional to displacement is the definition of SHM, and it produces the familiar sinusoidal oscillation.

When two identical waves travel in opposite directions on a string, they add up so that some points never move (nodes) and others oscillate the most (antinodes). That is a standing wave — it looks stationary but is actually two waves cancelling and reinforcing each other continuously.

Doppler effect: imagine an ambulance siren. As it rushes toward you, each successive sound wave crest is emitted from a position slightly closer to you, so the crests pile up — wavelength shortens — pitch rises. As it moves away, crests stretch out — pitch falls. The effect is purely geometric, not due to a change in the actual sound produced.