Clarity & Sting
Ever noticed how a bike’s hum shifts when you change gears? There’s a whole physics puzzle in those vibrations that we could dig into.
Yeah, the hum changes because the cadence and gear ratio shift the vibration frequency of the drivetrain. When you shift up, the chain moves faster over fewer teeth, so the tone rises. Switch down, it slows and the pitch drops. It’s basically the same principle as how a violin string changes pitch when you tighten or loosen it. Interested in exploring the math behind it?
Sounds good. Just keep the engine breathing steady, and we’ll get that math on the road.
Let’s map the cadence and gear ratios to vibration frequency. The chainring size, rear sprocket size, and pedal speed give us a base frequency; shifting changes the tooth count ratio, altering the vibration pitch. We can derive an equation for frequency as f = (cadence × teeth_chainring) / (teeth_sprocket × 60). That’s the core relationship we’ll work from.