Waves · Radar & Electromagnetic Spectrum
Radar & EM Spectrum Lab
Iret = PkS / 16π²d⁴
① pulse expanding — intensity at the front falls as P/4πr²
scene spacing is log-compressed — every number uses the real d
Try first: drag Distance d — watch dots land on −4 line.
Radar controls
Each drag of d lays a dot on the −4 line below.
The d⁴ machine — four steps, one per stage
①Intensity at target1.59×10⁻³ W m⁻²
I = P / 4πd² — first inverse-square trip
②Power intercepted1.59×10⁻³ W
P_int = I × S — target collects intensity × its area
③Re-emitted power4.77×10⁻⁴ W
P_re = k × P_int — target becomes a NEW point source
④Intensity back at transmitter3.80×10⁻¹³ W m⁻²
I_ret = P_re / 4πd² = PkS / 16π²d⁴ — second inverse-square trip
Re-emitted power = k × INTERCEPTED (I × S), not k × P.
Returned intensity vs distance — log–log
ⓘ more
Doubling d on the −2 line costs ×4 in intensity; on the −4 line it costs ×16. The white dot rides the single-trip curve with the outbound pulse front.
Pulse energy — E = mean power × pulse duration
E = P̄ × τ = 2.00×10⁶ W × 3.00×10⁻⁶ s = 6.00 J
Defaults match worked example: 2 MW × 3 µs = 6 J.
EM spectrum explorer — sweep λ from 10⁻¹⁴ m to 10³ m
band
Visible
λ / m
5.50×10⁻⁷
f = c/λ / Hz
5.45×10¹⁴
Visible band — 400 nm violet → 700 nm red
400 nm · f = 7.5×10¹⁴ Hz (violet, max f)700 nm · f = 4.3×10¹⁴ Hz (red, min f)
λ = 550 nm → green
EM wave structure — E ⊥ B ⊥ direction of travel
ⓘ more
- Transverse: E and B oscillate at right angles to the travel direction (+x) and to each other, in phase.
- No medium: nothing material oscillates — the fields themselves do, so EM waves cross vacuum.
- One speed: every band travels at c = 3.00×10⁸ m s⁻¹ in vacuum, from γ-rays to radio.
What this confirms — Wave Motion notes cards
- Radar / reflection — the d⁴ pattern. The four-step assembler chains two inverse-square trips into Iret = PkS/16π²d⁴ — the log–log plot shows your dragged points landing on slope −4, next to the −2 single-trip line.
- Receiver questions. Step ② is the whole trick: power collected by any surface = I × S (its area). The target then re-emits k × (I·S) — k × what it intercepted, never k × P.
- Electromagnetic wave. The 3D wave shows E ⊥ B ⊥ direction of travel, in phase, transverse, needing no medium, moving at c = 3.00×10⁸ m s⁻¹ in vacuum.
- EM spectrum. Sweeping the λ slider walks the fixed order γ → X-ray → UV → visible → IR → microwave → radio, with wavelength growing from 10⁻¹⁴ m to 10³ m and f = c/λ falling to match.
- Visible-band numbers. 400 nm violet ↔ 7.5×10¹⁴ Hz and 700 nm red ↔ 4.3×10¹⁴ Hz via f = c/λ — so the minimum visible frequency pairs with the longest wavelength (quiz chip).