Light and Sound Phenomena: Refraction, Doppler Shift, and Density
Refractive index, the Doppler effect, sound travel time, and specific gravity — four calculations describing how light and sound behave and how substances compare to water.
Light bending, sound shifting pitch, and sound traveling at a finite speed are all everyday phenomena with precise underlying formulas.
Refractive index: how much a material slows light down
Refractive index is n = c / v, the speed of light in a vacuum divided by its speed in the material. Light traveling at 200,000,000 m/s in a material gives a refractive index of about 1.499 — close to typical glass, which slows light to roughly two-thirds its vacuum speed.
The Doppler effect: why an approaching siren sounds higher-pitched
When a sound source moves toward a stationary observer, the perceived frequency increases according to the Doppler formula, which factors in the speed of sound and the source's speed relative to it — the same effect (in reverse) explains why the siren's pitch drops as it passes and moves away.
Sound travel time: turning a thunder delay into distance
Sound travels at about 343 m/s in air, so covering 1,000m takes roughly 2.92 seconds — the basis for the classic "count the seconds between lightning and thunder" trick, where roughly 3 seconds per kilometer (or 5 seconds per mile) estimates storm distance.
Specific gravity: comparing density to water
Specific gravity is a substance's density divided by a reference density (usually water at 1,000 kg/m³). A substance with 800 kg/m³ density has a specific gravity of 0.8, meaning it's less dense than water and would float in it.
Everyday phenomena, precisely described
Refraction, Doppler shift, sound propagation speed, and relative density all follow exact formulas behind what looks like ordinary experience. Try the refractive index calculator, Doppler effect calculator, sound travel time calculator, and specific gravity calculator.