9.1 Intensity of Waves

Waves are carriers of energy. The destructive power of earthquakes, the sensation of hearing, and the ability of a laser to cut material are all manifestations of the energy transported by waves. The intensity of a wave is the physical quantity used to measure this energy transfer.

Definition of Intensity

Intensity is defined as the power (P) transmitted per unit area (A), where the area is perpendicular to the direction of wave propagation.

Formula:

$I=\frac{P}{A}$

• $I$ = Intensity (Unit: Watts per square meter, W/m²)
• $P$ = Power (Unit: Watt, W)
• $A$ = Area (Unit: square meter, m²)

Since power is the rate at which energy is transferred ($P=E/t$), the formula can also be written as:

$I=\frac{E}{A\times t}$

• $E$ = Energy (Unit: Joule, J)
• $t$ = Time (Unit: second, s)

In simple terms, intensity measures how concentrated the energy flow of a wave is.

Derived Units→

Factors Affecting Intensity

1. Amplitude of the Wave

The intensity of a wave is directly proportional to the square of its amplitude. This is a crucial relationship in wave physics.

$I\propto (\text{Amplitude}{)}^2$

• Implication: Doubling the amplitude of a wave quadruples its intensity (and the energy it carries).
• Examples:
  • A high-amplitude earthquake wave causes more ground displacement and destruction.
  • A loud sound (high-amplitude sound wave) carries more energy and can damage hearing.

2. Time of Application

The total energy (E) delivered by a wave depends on the duration for which it acts. Longer exposure means more energy is transferred.

• Examples:
  • A longer exposure to sunlight transfers more solar energy.
  • Prolonged use of therapeutic ultrasound delivers more energy to the tissue.

3. Area Covered by the Wave

For a wave spreading out from a point source, the energy is distributed over an increasingly larger area. This causes the intensity to decrease as the distance from the source increases. For a point source, the intensity follows the inverse square law:

$I\propto \frac{1}{r^2}$

• Examples:
  • The intensity of an earthquake's seismic waves decreases as they spread out from the epicenter.
  • Sunlight focused by a magnifying glass onto a small spot has a very high intensity, enough to start a fire.

Wave intensity is a critical concept for quantifying the energy carried by waves. It explains why a focused laser can cut steel, why loud music can be harmful, and how the energy from an earthquake dissipates with distance.