Standing waves and harmonics are really related ideas, especially when we look at tuning forks.

When you hit a tuning fork, it vibrates and makes sound waves that move through the air. But what do standing waves have to do with this?

Understanding Standing Waves:
A standing wave happens when two waves with the same frequency and strength move in opposite directions and bump into each other. This creates parts that don’t move at all, called nodes, and parts that move the most, called antinodes.

Harmonics and Tuning Forks:
Harmonics are special frequencies where something can vibrate really well. For a tuning fork, the fundamental frequency (the first harmonic) is the lowest sound it makes when it vibrates. When you hit the fork, it vibrates at this lowest frequency and forms a standing wave pattern in the fork itself.

Each harmonic is a higher energy level. The second harmonic (the first overtone) has a frequency that is double the fundamental frequency, while the third harmonic has a frequency that is three times higher. You can think of this relationship like this:

If we use the formula:
$f_n = n \cdot f_1$

Here, $f_n$ is the frequency of the $n^{th}$ harmonic and $f_1$ is the first harmonic frequency.

To sum it up, standing waves form in tuning forks as they vibrate at harmonic frequencies. This helps them make beautiful and rich sounds!