What is the primary difference between Wave Power and Wave Intensity?

Power is the total energy emitted by a source per unit time (Watts), whereas Intensity is the power distributed over a specific unit area ($W m^{-2}$). Power is a property of the source, while intensity depends on the distance from that source.

How does the intensity of a plane wave compare to a spherical wave as distance increases?

For a plane wave, the area remains constant, so intensity does not decrease with distance (ideally). For a spherical wave, the area increases with $r^2$, so intensity decreases following the inverse square law ($1/r^2$).

If Wave A has twice the amplitude and twice the frequency of Wave B, what is the ratio of their intensities?

The intensity ratio is 16:1. Since $I \propto A^2$ and $I \propto f^2$, doubling both results in a factor of $2^2 \times 2^2 = 4 \times 4 = 16$.

What is a common error when calculating intensity at a distance $3r$ compared to distance $r$?

A common error is assuming a linear decrease and stating the intensity is $1/3$ of the original. Because of the inverse square law, the intensity is actually $1/3^2$, which is $1/9$ of the original value.

Why is it incorrect to use the formula $I = P / (4\pi r^2)$ for a laser beam?

A laser beam is highly directional and does not spread spherically in all directions. The $4\pi r^2$ formula specifically describes the surface area of a sphere, which only applies to uniform point sources.

What happens to the calculated intensity if you forget to convert a radius from centimeters to meters?

The resulting intensity will be incorrect by a factor of 10,000 ($100^2$). Since the unit is $W m^{-2}$, all dimensions must be in meters to maintain consistency with the Watt (Joule per second).

Define the 'Intensity' of a progressive wave.

Intensity is the power delivered per unit area, where the area is oriented perpendicular to the direction of wave energy transfer. It is measured in $W m^{-2}$.

State the mathematical relationship between Intensity ($I$) and Amplitude ($A$).

Intensity is directly proportional to the square of the amplitude ($I \propto A^2$). This means any change in amplitude has a squared effect on the energy delivered.

What is the formula for the intensity of a wave from a point source at a distance $r$?

The formula is $I = \frac{P}{4\pi r^2}$, where $P$ is the source power. This accounts for the energy spreading over the surface of a sphere.

Why does the intensity of a sound wave decrease as you move away from the speaker?

As the wave travels, the initial energy emitted by the speaker spreads over an increasingly large surface area. Since the total energy is spread thinner, the energy per unit area (intensity) must decrease.

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4. Electrons, Waves & Photons

Intensity of a Wave

Summary

Intensity is a fundamental physical quantity that describes the rate of energy transfer by a wave per unit area. It is governed by the power of the source and the geometry of the wave's propagation, typically following an inverse square relationship with distance and a square relationship with both amplitude and frequency.

1. Definition & Core Concepts

Intensity ( $I$ ) is defined as the amount of energy passing through a unit area perpendicular to the direction of wave propagation per unit time.
Since energy per unit time is equivalent to Power ( $P$ ), intensity is most commonly expressed as the ratio of power to area.
The standard SI unit for intensity is Watts per square meter ( $W m^{-2}$ ).

Fundamental Formula: $I = \frac{P}{A}$ where $P$ is the power in Watts and $A$ is the area in $m^2$ .

Diagram showing a point source emitting waves. As the distance doubles from r to 2r, the area the energy spreads over quadruples, illustrating the inverse square law.

2. Underlying Principles: Proportionality

3. The Inverse Square Law

4. Key Distinctions

5. Methods & Techniques: Ratio Calculations

6. Exam Strategy & Tips