We can see the wave equation, written as (v = f\lambda), in many everyday situations. Let’s break this down with some easy examples:

1. Sound Waves:

   • The speed of sound in the air is about 343 meters per second at 20°C.
   • If a sound has a frequency of 440 Hz, like the A4 music note, we can find the wavelength like this:
     (\lambda = \frac{v}{f} = \frac{343 \text{ m/s}}{440 \text{ Hz}} \approx 0.78 \text{ m})
   • So, the wavelength for a 440 Hz sound wave is about 0.78 meters.

2. Light Waves:

   • The speed of light in a vacuum is really fast—about (3 \times 10^8) meters per second.
   • For green light, which has a wavelength of 500 nanometers (nm), we can find the frequency:
     (f = \frac{v}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{500 \times 10^{-9} \text{ m}} \approx 6 \times 10^{14} \text{ Hz})
   • This means the frequency of green light is about (6 \times 10^{14}) Hz.

3. Water Waves:

   • In shallow water, waves can move at a speed of around 1.5 meters per second.
   • If these waves have a frequency of 0.5 Hz, we can calculate the wavelength as:
     (\lambda = \frac{v}{f} = \frac{1.5 \text{ m/s}}{0.5 \text{ Hz}} = 3 \text{ m})
   • This tells us that each wave crest is 3 meters apart.

These examples show how the wave equation works for sound, light, and water waves. They help us understand the basic qualities of waves in different environments.