Why pushing a bell does not produce a sound

Abstract

The difference between “beating” and “pushing” results in the perception that a push just makes an object move as a whole, while a beat also produces a sound. Through a detailed analysis of the physics underlying such everyday experiences, we identify the strength, the duration, and the softness of the applied contact force as the main (measurable) characteristics that mark such a difference. The strength determines the final velocity Δv achieved by the body. The duration 2τ corresponds to the time τℓ the sound takes to cross the body. The softness γ (a positive exponent) results from the shape in time of the contact force. These three elements make up the formula for the intensity of the sound produced. The relevant role of the softness is stressed and specific values are calculated for a thin metallic bar, which is chosen as the simplest possible model system.