demonstrations:ruler_vibration_pitch
Ruler Vibration Pitch
Materials: ★☆☆ Easy to get from supermarket or hardware store
Difficulty: ★☆☆ Can be easily done by most teenagers
Safety: ★☆☆ Minimal safety procedures required
Categories: Sound
Alternative titles: Table-Edge Ruler Oscillator
Summary
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.
Procedure
- 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.
- Start with an overhang of about 10 cm.
- Pull down gently on the free end and release to let it vibrate; listen to the pitch.
- Increase the overhang length in small steps and repeat, noting that the pitch lowers as length increases.
- Decrease the overhang length and repeat, noting that the pitch rises as length shortens.
- Try pressing down harder on the clamped section to increase stiffness and observe that the pitch rises.
- Optionally record pitches with a phone tuner app or count oscillations visually in slow motion.
Links
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:
Variations
- 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.
Safety Precautions
- 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.
Questions to Consider
- 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.)