7.1 Waves

7.1 Waves

A wave is a regular disturbance or variation that carries energy, which spreads out from the source. For example, energy is transferred from the Sun to the Earth in the form of light waves called electromagnetic waves. These waves can even travel through vacuum. However, in a medium, energy is transferred due to the regular and repeated disturbances that travel through the medium, making its particles to move up and down or back and forth (to and fro). Imagine a stone thrown into a pond of water (Fig. 7.1).

• The stone produces a disturbance (ripple) that travels through the water (medium).
• The water particles move up and down about their mean positions, creating a repeating pattern known as wave that spreads out.

The displacement of a particle of a wave is its distance in a specified direction from its rest / equilibrium position. If the displacement is plotted along the y-axis and the time in the direction of energy travel along the x-axis, we get a waveform as shown in Fig. 7.2.

The waves can be described by the following parameters:

1. Amplitude $(A)$: The maximum displacement of the wave (or particles of the medium) from its equilibrium position.

2. Frequency $(f)$: The number of oscillations or vibrations or cycles per second.

3. Wavelength $(\lambda)$: The distance between two consecutive similar points on the wave that are in phase.

4. Period $(T)$: The time taken by the wave to complete one oscillation or cycle. It is the reciprocal of the frequency $T = 1/f$.

5. Speed $(v)$: The speed at which the wave travels. If a wave crest moves one wavelength in one period of oscillation $T$, the speed is given by: $v = \lambda/T$ as $1/T = f$, so

6. Phase $(\theta)$: The relative position of a point on the wave at a given time.