Sensitivity and frequency response (A-level only): Definition of intensity.

The idea

Intensity is the power transferred per unit area perpendicular to the direction of energy flow, so I = P/A, measured in W m⁻². It is a scalar describing how concentrated a wave's energy is, not the total energy emitted. For a point source radiating uniformly in three dimensions, the same power spreads over a sphere of area 4πr², giving I = P/(4πr²); doubling distance quarters intensity. In hearing contexts, intensity relates to loudness through the decibel scale, where a tenfold intensity increase corresponds to about 10 dB. When a surface is tilted, use the component of area perpendicular to the beam. Always identify the power and the area at right angles to the flow before substituting values.

What earns the marks

• States that intensity is power per unit area, with area measured perpendicular to the direction of energy transfer.
• Recalls the equation I = P/A and uses consistent units, typically W m⁻².
• Applies the inverse-square relationship I = P/(4πr²) for a point source radiating uniformly in all directions.
• Explains that intensity decreases with distance because the same power is spread over an increasing spherical surface area.
• Distinguishes intensity from total power: a source may emit constant power while intensity at a detector falls with distance.
• Uses the decibel relationship qualitatively or quantitatively to link intensity ratios to loudness changes.

Common mistakes and how to put them right

• Using the total surface area of a sphere but forgetting the factor 4π, writing I = P/r².

  Put it right: The corrected form is I = P/(4πr²).

• Treating intensity as a vector and giving a direction.

  Put it right: Intensity is a scalar, although energy flow has a direction.

• Using the full area of a tilted surface rather than its component perpendicular to the beam.

  Put it right: The corrected approach uses A cos θ.

• Confusing intensity with amplitude.

  Put it right: Intensity is proportional to amplitude squared for a given wave.

Exam tips

• Write the defining equation before substituting numbers so the power and perpendicular area are clearly identified.
• When a question mentions a point source, check whether the inverse-square law applies before calculating.
• Convert distances to metres and areas to square metres before evaluating intensity to avoid unit errors.
• Link any calculated intensity ratio to the decibel scale if the question asks about loudness or hearing.