When you study waves in Grade 10 physics, one important idea you will learn about is how frequency and wavelength are connected. You can use a simple wave equation to explore this relationship:

$v = fλ$

Here is what the symbols mean:

• $v$ is the speed of the wave (how fast it moves),
• $f$ is the frequency (how many waves pass a point in one second), and
• $λ$ (lambda) is the wavelength (the distance between one wave and the next).

Understanding Frequency and Wavelength

1. Frequency ($f$):

   • Frequency is measured in hertz (Hz). One hertz means one wave passes in one second.
   • For example, if a wave has a frequency of 2 Hz, it means two waves pass a point every second.

2. Wavelength ($λ$):

   • Wavelength is the length of one complete wave.
   • For instance, if the distance from the top of one wave to the top of the next wave is 3 meters, then the wavelength is 3 meters.

How Frequency and Wavelength Work Together

Let’s break down what happens to wavelength when frequency changes:

• When Frequency Increases:

  • If more waves pass by each second, the frequency is higher.
  • The speed of a wave usually stays the same in a certain medium, like when sound travels through air or light travels through space.
  • So, if the frequency goes up ($f$ increases), the wavelength ($λ$) must go down to keep the speed ($v$) the same.

  For example, if a wave's frequency goes from 10 Hz to 20 Hz and the speed is 340 m/s (the speed of sound), we can find the new wavelength:

  $v = fλ \implies 340 = 20λ$

  If we solve for $λ$, we find $λ = 17$ meters.

• When Frequency Decreases:

  • If fewer waves pass by each second, the frequency is lower.
  • In this case, the wavelength increases to keep the wave speed the same.

  For example, if the frequency drops to 5 Hz, we solve again:

  $340 = 5λ$

  This tells us $λ = 68$ meters.

Summary

In short, there's an important link between frequency and wavelength:

• When frequency increases, the wavelength gets shorter.
• When frequency decreases, the wavelength gets longer.

Understanding this relationship is key to knowing how waves act in different situations. It's important for many things, like music and telecommunications. So the next time you see a wave, think about how its frequency and wavelength work together!