Ruler Vibration Pitch

A ruler held to the edge of a table is bent and released to vibrate. Changing the overhang length or how firmly it is clamped changes the vibration frequency and the sound pitch.

1. Place a flat ruler so part of it extends past the edge of a sturdy table and hold the inboard section firmly with one hand or a heavy book to clamp it.
2. Start with an overhang of about 10 cm.
3. Pull down gently on the free end and release to let it vibrate; listen to the pitch.
4. Increase the overhang length in small steps and repeat, noting that the pitch lowers as length increases.
5. Decrease the overhang length and repeat, noting that the pitch rises as length shortens.
6. Try pressing down harder on the clamped section to increase stiffness and observe that the pitch rises.
7. Optionally record pitches with a phone tuner app or count oscillations visually in slow motion.

Vibrations in a steel ruler - Knowledge Media Institute (KMi) @Open University:

How tones of different heights are created? explained simply and clearly with a swinging ruler - physikdigital:

• Compare plastic, wooden, and metal rulers of the same length.
• Add small masses (paper clips) near the tip and observe the pitch decrease.
• Flip the ruler so different thickness edges overhang and compare pitch.
• Measure frequency vs overhang length and plot them.
• Use a meter stick or thin strip of metal or acrylic as a longer vibrating beam.

• Keep fingers clear of the snapping tip to avoid minor stings.
• Secure the clamp with a heavy book or your non-dominant hand so the ruler does not fly off.
• Use safety glasses if using brittle plastic rulers that might crack.
• Do not overbend the ruler to prevent breakage.

• What happens to pitch when the overhang length increases? (Pitch decreases because the vibrating section is longer and less stiff.)
• How does material affect the sound? (Stiffer, denser materials tend to produce higher frequencies for the same geometry and may sound louder.)
• Why does clamping force change the pitch? (Stronger clamping increases effective stiffness near the support, raising frequency.)
• Which physical quantities mainly set the frequency of a vibrating ruler? (Length, thickness/width and material stiffness, and mass per length.)
• How is this similar to string instruments? (Shorter, tighter, or stiffer vibrating elements give higher pitch, analogous to fretting or tightening a string.)