Transverse Pulses & Waves

≈ 30 min

From a pulse to a wave

Flick one end of a stretched rope once and a single hump travels along it - that is a pulse. Keep shaking the end up and down steadily and you send a continuous train of pulses: a wave.

In a transverse wave the particles of the medium move perpendicular to the direction the wave travels. Each bit of rope only moves up and down, yet the shape moves sideways along the rope. The wave carries energy from one place to another without carrying the medium along with it.

The vocabulary of a wave

Amplitude ( $A$ ): the maximum displacement from the rest position. Bigger amplitude means more energy.
Wavelength ( $\lambda$ ): the distance of one complete wave - for example crest to next crest.
Period ( $T$ ): the time for one complete wave to pass a point, in seconds.
Frequency ( $f$ ): the number of complete waves per second, in hertz ( $\text{Hz}$ ).

Period and frequency are reciprocals:

f = \frac{1}{T} \qquad T = \frac{1}{f}

The speed of the wave links these together:

v = f\lambda

In a transverse wave on a rope, how do the particles of the rope move relative to the direction the wave travels?

In the same direction as the wave

Perpendicular (at right angles) to the direction of the wave

In circles that grow larger over time

They do not move at all

A water wave has a frequency of $4\,\text{Hz}$ and a wavelength of $0.5\,\text{m}$ . Calculate the speed of the wave in $\text{m/s}$ .

A wave has a period of $0.25\,\text{s}$ and travels at $8\,\text{m/s}$ . Calculate its wavelength in metres.