Frequency, Speed and Intensity

The wave equation —

v = fλ

The speed of a wave is set by the medium, not by the source. When a wave passes into a different medium its speed changes and its wavelength changes with it, but the frequency stays the same, because the source is still oscillating at the same rate.

Example: this is the key to refraction. Light entering glass slows down, so since f cannot change, λ must decrease. Any explanation of refraction that has the frequency changing is wrong.

Period and frequency — f = 1/T, so a wave of frequency 250 Hz has a period of 1/250 = 4.0 × 10⁻³ s.

Intensity — the power per unit area received perpendicular to the direction of travel:

I = P / A

measured in W m⁻².

The inverse square law — for a point source radiating uniformly, the power spreads over the surface of a sphere of area 4πr², so

I ∝ 1 / r²

Doubling the distance from a source reduces the intensity to a quarter, not a half. Nothing is absorbed in this model; the same power is simply spread over four times the area.

Intensity and amplitude — intensity is proportional to the square of the amplitude:

I ∝ A²

So doubling the amplitude of a wave quadruples the energy it delivers per second per unit area. This is why a wave of twice the amplitude is not twice as loud or twice as bright.

Example: combining the two relationships is a standard exam step. If the distance from a lamp is doubled, the intensity falls to a quarter, so the amplitude of the light wave falls to a half — since I ∝ A², halving A quarters I.