======Ruler Vibration Pitch======


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**Alternative titles:** Table-Edge Ruler Oscillator
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====Summary====                   
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====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: 
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How tones of different heights are created? explained simply and clearly with a swinging ruler - physikdigital: 
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====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.)