Final answer:
An object made of a stiff material vibrates at a higher frequency because it has greater elasticity, enabling it to rapidly return to its original shape and undergo quicker oscillations. Higher stiffness implies a shorter period and therefore a higher frequency of vibration. The correct answer is c.Stiff materials have higher elasticity.
Step-by-step explanation:
You expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material because stiff materials have higher elasticity. The stiffness of material generally indicates how resistant it is to deformation when force is applied.
The higher the elasticity, the greater the material's ability to return to its original shape after being deformed. This property contributes to the material's ability to vibrate at higher frequencies because it can more quickly return to its original shape after an external force has been removed, allowing for more rapid oscillations.
Another aspect to consider is that an object's vibration frequency is related to the stiffness and the mass of the oscillating system. According to the concept of simple harmonic motion, a stiffer object typically has a shorter period of oscillation, meaning it completes each cycle of vibration more quickly and thus has a higher frequency.
Conversely, a more spongy or less stiff material tends to absorb and dissipate energy, leading to slower oscillations and a lower frequency of vibration.