To make the wave equation easier to understand and see how speed, wavelength, and frequency all work together, let’s break it down step by step.

The wave equation looks like this:

$v = f \lambda$

Here’s what each part means:

• $v$ is the wave speed.
• $f$ is the frequency, which tells us how many waves pass a point in one second.
• $\lambda$ is the wavelength, or the distance between two wave peaks.

Let's Understand Each Part

1. Frequency ($f$):

   • This is measured in hertz (Hz).
   • It shows how many waves happen in one second.
   • For example, if a wave moves up and down 5 times in one second, its frequency is $5 \, \text{Hz}$.

2. Wavelength ($\lambda$):

   • This measures the distance from one peak of a wave to the next peak.
   • If you measure the distance between two wave tops and get $2 \, \text{meters}$, then $\lambda = 2 \, \text{m}$.

3. Wave Speed ($v$):

   • This tells us how fast the wave moves.
   • It is usually calculated in meters per second ($\text{m/s}$).

Real-Life Examples

• Sound Waves:

  • In the air, sound waves travel at about $340 \, \text{m/s}$.
  • If a sound has a frequency of $170 \, \text{Hz}$, we can find its wavelength like this:

  $\lambda = \frac{v}{f} = \frac{340 \, \text{m/s}}{170 \, \text{Hz}} = 2 \, \text{m}$

  So, the wavelength is $2$ meters.

• Water Waves:

  • If a water wave has a frequency of $1 \, \text{Hz}$ and moves at $3 \, \text{m/s}$, its wavelength will be:

  $\lambda = \frac{v}{f} = \frac{3 \, \text{m/s}}{1 \, \text{Hz}} = 3 \, \text{m}$

  Here, the wavelength is $3$ meters.

By looking at these examples, we see how these parts connect. This makes the wave equation a useful tool for understanding how waves behave!