Define amplitude, wavelength, frequency and period, distinguish transverse and longitudinal waves, and apply the wave equation $v = f\lambda$ and the period-frequency relationship $T = 1/f$.

What this topic is asking

This dot point opens the waves strand by defining the quantities that describe any wave and linking them with the wave equation. The Physical Setting/Physics course asks you to define amplitude, wavelength, frequency and period, to distinguish transverse from longitudinal waves, and to apply $v = f\lambda$ and $T = \dfrac{1}{f}$. The Regents tests these as definitions, diagram-reading, and calculations linking speed, frequency and wavelength.

The properties of a wave

These quantities describe any periodic wave. The amplitude relates to the energy the wave carries (a louder sound or brighter light has a larger amplitude), while the frequency relates to pitch for sound or color for light. Frequency and period are reciprocals, so a higher frequency means a shorter period. Reading these off a wave diagram, distinguishing wavelength (a distance) from period (a time), is a common Regents skill.

Transverse and longitudinal waves

The distinction matters because some behaviors (like polarization) occur only for transverse waves. On the Regents, light and other electromagnetic waves are always transverse and can travel through a vacuum, while sound is longitudinal and needs a medium (it cannot travel through a vacuum).

The wave equation

The wave equation ties the three central quantities together: any one can be found from the other two. A key consequence is that in a given medium the wave speed is fixed, so frequency and wavelength are inversely related: a higher-frequency wave has a shorter wavelength. The frequency is set by the source and does not change when a wave passes into a new medium; the speed and wavelength change together to keep $v = f\lambda$ satisfied (the basis of refraction).

Reference Tables note

The Reference Tables print the wave equation $v = f\lambda$ and the period-frequency relationship $T = \dfrac{1}{f}$ in the Waves section. The definitions of amplitude, wavelength, frequency and period, and the transverse-longitudinal distinction, are recall items. The speed of light $c = 3.00 \times 10^8$ m/s in the constants list is the wave speed for all electromagnetic waves in a vacuum, used with $v = f\lambda$ for the electromagnetic spectrum.

Try this

Q1. State the difference between a transverse and a longitudinal wave. [2 points]

• Cue. Transverse: the medium vibrates perpendicular to the wave direction. Longitudinal: the medium vibrates parallel to the wave direction.

Q2. A wave has a frequency of $8.0$ Hz and wavelength $0.50$ m. Calculate its speed. [2 points]

• Cue. $v = f\lambda = (8.0)(0.50) = 4.0$ m/s.