3. Frequency, Speed and the Wave Equation

Frequency is how many waves pass a point each second, measured in hertz (Hz). For a wave traveling at fixed speed, higher frequency means shorter wavelength.

The relationship is:
\[ v = f \lambda \]
where \(v\) is wave speed, \(f\) is frequency, and \(\lambda\) is wavelength.

Deep explanation. Frequency is the number of wave cycles passing a point each second. It is measured in hertz, where \(1\text{ Hz}\) means one cycle per second. Wavelength is the length of one cycle. Wave speed connects them: \(v = f\lambda\).

For a wave moving at a fixed speed, frequency and wavelength move in opposite directions. If frequency increases, more cycles must fit into the same distance per second, so wavelength decreases. If wavelength increases, fewer cycles pass each second, so frequency decreases.

Worked example. A wave has frequency \(4\text{ Hz}\) and wavelength \(3\text{ m}\). Its speed is \(v = 4 \times 3 = 12\text{ m/s}\). If speed is \(20\text{ m/s}\) and frequency is \(5\text{ Hz}\), wavelength is \(20/5 = 4\text{ m}\).

⚠️ Common misconception: frequency and wavelength always increase together. At the same speed, they move in opposite directions.

💡 Tip: more waves per second means each wave is shorter.