# Why pushing a bell does not produce a sound

## TL;DR

This paper analyzes the physics behind why pushing objects does not produce sound, identifying key measurable contact force characteristics that influence sound production.

## Contribution

It introduces a detailed physical model linking contact force parameters to sound intensity, emphasizing the role of softness in sound generation.

## Key findings

- Strength determines the final velocity of the object.
- Duration relates to the sound crossing time of the object.
- Softness significantly affects the sound intensity, with specific values calculated for a metallic bar.

## Abstract

The difference between "beating" and "pushing" results in the perception that a push just makes the object move as a whole, while a beat produces also a sound. Through a detailed analysis of the physics underlying such everyday experiences, we identify the \emph{strength}, the \emph{duration} and the \emph{softness} of the applied contact force, as the main (measurable) characteristics that mark such difference. The strength determines the final velocity $\Delta v$ achieved by the body. The duration $2\tau$ compares to the time $\tau_\ell$ the sound takes to cross the body. The softness $\gamma$ (a positive exponent) results from the shape in time of the contact force. Those three elements enter 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, chosen as the simplest possible model system.