Every wave obeys the same relationship between how fast it travels, how often it oscillates and how long each cycle is in space. It follows directly from the definitions: in one period the wave advances exactly one wavelength.
Speed is set by the medium, not the source
This is the point students most often miss. Sound travels at about 343 m/s in air at 20 °C whatever note you play; light travels at 3.00 × 10⁸ m/s in a vacuum whatever its colour. When a wave crosses into a different medium its speed changes and its wavelength changes with it — but its frequency does not, because the source is still oscillating at the same rate. Frequency is the property that survives refraction, which is why a sound is the same pitch underwater.
Some reference speeds
| Medium | Wave | Speed |
|---|---|---|
| Air at 20 °C | Sound | 343 m/s |
| Water | Sound | 1480 m/s |
| Steel | Sound | ≈5900 m/s |
| Vacuum | Light | 2.998 × 10⁸ m/s |
| Glass (n ≈ 1.5) | Light | ≈2.0 × 10⁸ m/s |
Why quarter wavelengths keep appearing
Antennas, organ pipes and acoustic treatment all key off fractions of a wavelength, because that is where standing-wave nodes and antinodes fall. A quarter-wave antenna for 2.4 GHz Wi-Fi is about 31 mm long, which is why the antenna in your router is the size it is.