14.1 Introduction

A wave is a disturbance which transfers energy from one part of a medium to another part without actual transfer or flow of matter as a whole. In the context of waves, matter refers to the physical substance-atoms, molecules, or particles-that makes up a medium (such as water, air, or a string) through which a wave travels. We are all familiar with water waves, sound waves and light waves. These waves occur when a system is disturbed from its equilibrium position and this disturbance travels from one place to another.

In other words, “a wave is any disturbance from a normal or equilibrium condition that propagates without the transport of matter. In general, a wave transports both energy and momentum.”

Particles vibrate, they do not travel:

As a wave passes, the individual particles of the medium vibrate around a fixed position, transferring energy to neighboring particles, but the particles themselves do not move from one end of the medium to the other.

Net Mass Transport:

The phrase “without…transfer of matter” means that there is no net displacement of the medium itself; the matter stays in its general location.

Examples: In a water wave, the water molecules move up and down, but the water itself does not flow forward; in a sound wave, air molecules compress and vibrate, but they do not travel with the sound.

The Mechanism of Energy Transfer:

The reason matter doesn’t move “as a whole” is due to the elastic properties of the medium.

• The Disturbance: When you pluck a string or speak into the air, you provide work (energy) to the first set of particles.
• The Coupling: Because particles are connected by intermolecular forces (acting like tiny springs), the first particle pulls on the second.
• The Restoration: As the first particle passes the energy to the second, the medium’s elasticity pulls the first particle back toward its equilibrium position.

By the time the “wave” has passed, every particle has returned to where it started, but the energy has moved far downstream.

Transport of Momentum:

Waves transport momentum (\(p\)). This is a deeper physics concept: even though a particle’s average displacement is zero over one full cycle, it possesses instantaneous momentum as it moves. When a wave hits a surface (like light hitting a solar sail or sound hitting an eardrum), it exerts radiation pressure. This proves that waves carry the “push” of momentum without needing to deliver a physical “slug” of matter to the target.

Misconception: Many people think that water waves push water from one direction to another. In fact, the particles of water tend to stay in one location, save for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water stays in one place. If you feel yourself pushed in an ocean, what you feel is the energy of the wave, not a rush of water.

What is wave energy?

The energy in water waves primarily comes from wind blowing across the surface of the water; as the wind interacts with the water, it transfers its kinetic energy, creating waves that propagate across the ocean surface. Wave energy (or wave power) harnesses the ocean’s waves to generate energy by converting a wave’s kinetic energy into electricity. Wave power is a form of renewable and sustainable energy that’s often overlooked but has immense potential.

Key points about water wave energy:

Source of wind energy: The wind itself is driven by the sun’s heat, making wave energy an indirect form of solar energy.

Mechanism: Friction between the wind and water surface causes the water to move in a circular motion, forming waves.

Wave characteristics: The strength of the wind and the duration it blows over the water determine the size and energy of the waves.

What is wave motion?

A wave motion is a means of transferring energy and momentum from one point to another without the actual transport of matter between two points. Transmission of energy over considerable distances is possible through wave motion. 

The simplest waves repeat themselves for several cycles and are associated with simple harmonic motion. Let us start by considering the simplified water wave in Figure 2. The wave is an up-and-down disturbance of the water surface. It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The time for one complete up and down motion is the wave’s period \(T\). The wave’s frequency is
\(
f=\frac{1}{T}
\)
, as usual. The wave itself moves to the right in Figure 2. This movement of the wave is actually the disturbance moving to the right, not the water itself (or the bird would move to the right). We define wave velocity \(v_w\) to be the speed at which the disturbance moves. Wave velocity is sometimes also called the propagation velocity or propagation speed because the disturbance propagates from one location to another.

The water wave in the figure also has a length associated with it, called its wavelength \(\lambda\), the distance between adjacent identical parts of a wave. ( \(\lambda\) is the distance parallel to the direction of propagation.) The speed of propagation \(v_{\mathrm{w}}\) is the distance the wave travels in a given time, which is one wavelength in the time of one period. In equation form, that is
\(
v_{\mathrm{w}}=\frac{\lambda}{T}
\)
\(
\text { or } v_{\mathrm{w}}=f \lambda \quad [f=\frac{1}{T}]
\)
This fundamental relationship holds for all types of waves. For water waves, \(v_{\mathrm{w}}\) is the speed of a surface wave; for sound, \(v_{\mathrm{w}}\) is the speed of sound; and for visible light, \(v_{\mathrm{w}}\) is the speed of light.