Sound Wave Modeler

Trigonometry · Axiom Academy

Discover how sine waves create the sounds you hear every day. Adjust frequency and amplitude to see and hear trigonometry in action! Every sound you hear—from music to voices to car horns—is actually a vibration traveling through the air . These vibrations can be perfectly described by sine waves from trigonometry! A Pure Tone (440 Hz - Musical Note "A") This is what a sine wave looks like Higher amplitude = Louder sound Lower amplitude = Quieter sound Higher frequency = Higher pitch Lower frequency = Lower pitch Use the sliders below to adjust the amplitude (volume) and frequency (pitch) of a sine wave. You can both see and hear the changes! Real-world sounds aren't just single sine waves—they're combinations of multiple frequencies ! This is why a piano sounds different from a guitar even when playing the same note. When you combine harmonics (multiples of the fundamental frequency), you create richer sounds! This is why musical instruments have their unique timbres—each instrument emphasizes different harmonics. Now that you've explored sound waves, let's see if you can predict what happens! If you double the frequency of a sound wave, what happens to its pitch? Where A is amplitude, f is frequency, and t is time Each doubling of frequency raises the pitch by one octave 440 Hz → A4 (one octave higher) 880 Hz → A5 (two octaves higher) Sound is a Sine Wave Pure tones are perfectly described by y = A sin(2πft)

This is the written version of the interactive lesson above. See the full Trigonometry course.