Topic 14.1 Properties of Wave Pulses and Periodic Waves: describe transverse and longitudinal waves and apply v = f lambda to periodic waves.

What this topic is asking

The College Board (Topics 14.1 and 14.2) want you to describe wave pulses and periodic waves, distinguish transverse from longitudinal waves, and apply the wave equation $v = f\lambda$ to relate speed, frequency and wavelength.

What a wave is

The defining feature of a wave is that it moves energy, not matter. A cork floating on water bobs up and down as a wave passes but stays roughly in place; the wave moves on, the water does not. This is true of every wave: sound carries energy through air without blowing the air across the room, and a wave on a rope travels along it while each bit of rope merely moves up and down. Keeping "energy travels, medium oscillates" clear is the conceptual heart of the topic.

Transverse and longitudinal waves

The two wave types differ only in the direction of the oscillation relative to travel. Transverse waves have crests and troughs (the string moves up and down while the wave goes sideways); longitudinal waves have compressions and rarefactions (the air bunches and spreads while the sound moves forward). Light is transverse (which is why it can be polarized, Topic 14.3); sound is longitudinal (which is why it needs a medium and cannot be polarized).

The wave equation

A periodic wave repeats in space (over one wavelength $\lambda$) and in time (over one period $T = 1/f$). In one period the wave advances exactly one wavelength, so its speed is

This single relation ties the three quantities together. The crucial subtlety is that the speed is set by the medium, not by the source: a sound wave travels at the same speed whatever its pitch. So when the source changes the frequency, the wavelength adjusts to keep $v$ constant, higher frequency means shorter wavelength. The amplitude (maximum displacement) sets the wave's energy and loudness or brightness, independent of frequency. The strategic role of this topic is that it establishes the vocabulary and the $v = f\lambda$ relation used throughout the unit: the boundary behavior of Topic 14.3, the wave nature of light in Topic 14.4, the Doppler shifts of Topic 14.5, and the interference of Topics 14.6 to 14.9 all build on these definitions.

Try this

Q1. A wave travels at $12$ m/s with a wavelength of $3.0$ m. Calculate its frequency. [2 points]

• Cue. $f = v/\lambda = 12/3.0 = 4.0$ Hz.

Q2. State whether sound is a transverse or longitudinal wave. [1 point]

• Cue. Longitudinal (the air oscillates parallel to the direction of travel).