PhysicsLab

Intensity & Spreading Lab

H2 Physics · Waves — one source power P, four geometries, four spreading laws

I vs r — all four geometries, relative to the value at 1 m

spherehemisphereripplebeam
ⓘ more

Normalised to I(1 m) so all four overlay. Hemisphere is dashed — same 1/r² shape as the sphere, but its absolute I is ×2 at every r. Flip to log–log to see the slopes.

A vs r — amplitude, relative to 1 m (A ∝ √I)

ⓘ more

Same overlay for amplitude: A ∝ 1/r (sphere, hemisphere), 1/√r (ripple), constant (beam) — log–log slopes −1, −½, 0.

Try first: press r ×2 — watch I divide by 4.

Geometry — the core control

I = P / 4πr²

A ∝ 1/r

energy spread over a sphere of area 4πr²

Valid for: point source · uniform emission · no absorption

Controls

At the detector

I (W/m²)
6.37e-3
A(r) / A(1 m)
0.200
√( I(r) / I(1 m) )
0.200
P_rx = I × A_det
1.59e-3 W

Middle rows always agree: A ∝ √I.

Power through the current wavefront

wavefront radius
0.2 m
area 4πr²
0.5 m²
I × area
2.000 W
source P
2.000 W

Equal at every radius — spread thinner, never lost.

What this confirms
  • ›“Intensity, I” — I is rate of energy per unit area: every I readout here is literally P divided by the wavefront it crosses.
  • ›“Geometry decides the law” — the toggle proves each case: sphere 1/r², hemisphere 1/r² at double strength, ripple 1/r, beam constant — log–log slopes −2, −1, 0.
  • ›“The intensity chain from SHM” — A ∝ √I: the A readout and √(I/I₁) stay identical no matter what you drag.
  • ›“Receiver questions” — the area ×2 button doubles power collected while I sits still: detector size changes P_rx, never intensity.
  • ›“Boundary/dilution: energy NOT lost” — I × wavefront area equals P exactly as the shell expands: dimmer only because the same power is spread thinner.
  • ›“Proportionality → ratio, always” — the doubling buttons answer with pure ratios (÷4, ÷2, ×2) — no absolute numbers needed, exactly how exam questions want it.