Read the wavelength, photon energy and propagation delay of an electromagnetic wave in the sandbox, and predict — before you read them off the screen — the wavelength at two very different frequencies, the energy a photon of green light carries, and how long a signal takes to cross one kilometre.
Everything on the spectrum obeys one relation: λ = c/f. Because c is fixed, wavelength and frequency are inverses — raise the frequency and the wave shrinks in exact proportion, so 100 MHz in the VHF FM band and 2.4 GHz in the UHF Wi-Fi band are worlds apart in size. The same wave carries a photon energy E = h·f and travels at c, so a distance d costs a delay t = d/c. Reading those numbers off a live wave — instead of taking them on faith — is how the spectrum stops being a chart and becomes something you can compute.
Open the sandbox. It opens on a single source in a vacuum (refractive index n = 1), so a Reset gets you close. For this lab, drag the Frequency slider until the readout reads the value each step names, and leave the refractive index at 1. Each step names the one knob to move; leave everything else alone.
Frequency -> set per step (100 MHz, 2.4 GHz, then green light) n -> 1 (vacuum)
Distance -> 1 km (feeds only the delay, used in Step 4)
Watch the Wavelength λ, Photon energy E and Propagation delay t readout cards — every number you predict is printed there.
Set the Frequency slider so the readout shows 100 MHz, with n = 1. The wave equation says λ = c/f with c = 299792458 m/s. Predict the wavelength in metres, then read the Wavelength λ card.
The card reads λ = 2.998 m — c/f = 299792458 / 1e8. A three-metre wave, which is why 100 MHz FM antennas are about a metre long.
Now set the Frequency to 2.4 GHz — the Wi-Fi band, 24 times higher than before. Wavelength and frequency are inverse, so predict how much shorter the wave gets and its length in metres; then read the Wavelength λ card.
The card reads λ = 0.1249 m — about 12.5 cm. Raising the frequency 24× shrank the wave by exactly 24× (from 2.998 m), because λ = c/f is a pure inverse.
Slide the Frequency all the way up into visible light, 5.4×10¹⁴ Hz — green light. The same wave carries a photon energy E = h·f, read in electronvolts. Predict the photon energy, then read the Photon energy E card.
The card reads E = 2.23 eV — h·f divided by the electronvolt. A single visible-light photon carries millions of times the energy of a 2.4 GHz Wi-Fi photon, because energy rises with frequency.
Set the Distance slider to 1 km. The wave travels at c, so it costs a one-way delay t = d/c — independent of frequency. Predict the delay in microseconds, then read the Propagation delay t card.
The card reads t = 3.336 µs — d/c = 1000 / 299792458. Light crosses a kilometre in about three and a third microseconds, and it does not matter one bit what the frequency was.
Everything above is waiting in the sandbox. Drag the Frequency slider across the whole spectrum and watch the wave pack in cycles while the band marker climbs, raise the refractive index to slow the wave and shorten its wavelength while the frequency holds, and stretch the distance to watch the delay grow.
- Read λ = 2.998 m at 100 MHz — c/f with c exact
- Saw 2.4 GHz give λ = 0.1249 m — a 24× higher frequency, a 24× shorter wave
- Found a green-light photon at E = 2.23 eV, h·f in electronvolts
- Measured the delay across a kilometre, t = 3.336 µs (d/c), the same at any frequency
- Every value you predicted is the demo's own exact arithmetic, not a picture