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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.

Frequency depends on the force constant and the force constant is related to the stiffness of the system. So, stiff material vibrates at a higher frequency than spongy material.

See the step by step solution

## Step 1: Relationship of the frequency with force constant

The frequency of a simple harmonic oscillator is given as follows,

$${\rm{f = }}\frac{{\rm{1}}}{{{\rm{2}}\pi }}\sqrt {\left( {\frac{{\rm{k}}}{{\rm{m}}}} \right)}$$

Here, k is the spring constant and m is the mass of the system.

## Step 2: Relation of spring constant and stiffness

The force constant $${\rm{k}}$$ is a measure of the stiffness of the system and it has a different value for different materials. The larger the spring constant, the stiffer will be the system and it is difficult to stretch that material.

It can be observed that the frequency is related to the stiffness of the system in the way that the frequency $$f$$ is directly proportional to the force constant, k. A stiff object has a large spring constant and so the faster it vibrates.

Thus, an object made of stiff material vibrates at a higher frequency than a similar object made of a spongy material (less stiffness).