The link between how tall a sound wave is (amplitude) and how loud it sounds is really interesting! Let me break it down for you:

1. What is Amplitude?
   Amplitude refers to how tall a sound wave is.
   Imagine the waves in the ocean. The higher the wave, the more energy it has.

2. What is Sound Loudness?
   When we talk about loudness, we mean how strong a sound feels to our ears.
   It’s all about how we perceive it!
   As the amplitude gets taller, the sound feels louder.

3. The Math Behind It
   Loudness has to do with sound intensity.
   Intensity depends on the square of the amplitude.
   So, if you make the amplitude twice as tall, the intensity—and the loudness—actually becomes four times greater!
   Here’s a simple way to explain it:

   $I \propto A^2$

   In this formula, $I$ stands for intensity and $A$ is the amplitude.

To sum it up, higher amplitudes mean louder sounds. That’s why concerts feel so powerful!