Temperature decreases (gets colder) resonant frequencies decreases.. WHY?

resonant frequency of what?

If it is a steel guitar string, the tension increases as the wire tries to contract and the frequency increases, not decreases.
However if it is an organ pipe, the air temp decreases and speed of sound decreases and frequency decreases.

The question goes like this:

The original air-filled apparatus now suffers a temp decrease of 40 degrees C, do the resonant frequencies decrease of increase? Give your reasoning

Well, that is my second example above

The resonant frequency of an object refers to the natural frequency at which it vibrates when excited or disturbed. This frequency is dependent on the physical properties of the object, such as its mass, stiffness, and length.

When the temperature decreases, it affects the physical properties of the object and, consequently, its resonant frequency. Here's an explanation of why this happens:

1. Thermal Expansion: Most objects expand or contract when exposed to temperature changes. As temperature decreases, the object contracts, resulting in a decrease in its dimensions. This change in dimensions alters the stiffness and mass distribution of the object, leading to a change in its resonant frequency.

2. Material Properties: Temperature can also influence the mechanical properties of materials. For instance, some materials become stiffer as the temperature decreases. As stiffness affects the resonant frequency, a stiffer material will have a lower resonant frequency.

To summarize, when the temperature decreases, it causes the object to contract and potentially becomes stiffer, which alters its physical properties. Since resonant frequency depends on these properties, a decrease in temperature leads to a decrease in resonant frequency.