14.1 Properties of Wave Pulses and Waves

Flick one end of a stretched rope once and a single bump runs down it. That's a wave pulse: one disturbance moving along. Keep shaking the end back and forth and you get a wave, a repeating disturbance with a regular wavelength and frequency.

In both cases, energy moves from your hand to the far end, but the rope itself doesn't travel. Each bit of rope moves a little and returns to where it started. The same is true of a stadium wave: the wave goes around the stadium, but every fan stays in their seat.

A mechanical wave is a disturbance of a material, so it needs a medium: a string, air, water, the ground. Sound can't cross the vacuum of space because there's nothing there to vibrate.

An electromagnetic wave, such as light or radio, is a pattern of changing electric and magnetic fields. It needs no medium and travels through empty space at c = 3.00 × 10⁸ m/s. That's how sunlight reaches Earth.

In a transverse wave, the medium moves perpendicular to the direction the wave travels. Shake a rope up and down and the wave runs sideways along it. Waves on strings and all electromagnetic waves are transverse.

In a longitudinal wave, the medium moves back and forth parallel to the direction the wave travels. Push and pull one end of a Slinky and you'll see bunched-up regions and spread-out regions travel along it.

Sound is a longitudinal wave. A speaker cone pushes air molecules together, making a compression (higher pressure), then pulls back, making a rarefaction (lower pressure). These pressure regions travel outward; the air molecules just jiggle back and forth in place.

Wave speed is set by what kind of wave it is and what it travels through, not by how you shake the source. For a string, the speed depends on the tension $F_T$ and the mass per unit length $\frac{m}{\ell}$:

$$v_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}}$$

A tighter string pulls back harder, so waves move faster. A heavier string has more inertia, so waves move slower. Shaking your hand faster makes more waves per second, but it doesn't change their speed.

The speed of sound in a given material rises with temperature. In air it's about 343 m/s at room temperature, a bit faster on a hot day. Sound also generally travels faster in liquids and solids than in air.

Amplitude is the maximum displacement of the medium from its resting position: the height of a crest on a rope. For a sound wave, you can describe amplitude as the biggest rise or drop in pressure above or below normal air pressure.

A bigger amplitude means the wave carries more energy. For sound, a bigger amplitude is heard as a louder sound. Amplitude doesn't affect the wave's speed.