# Energy density distribution of a vibrating string

• slcoleman
In summary, the conversation is about finding an equation to describe the energy distribution of a vibrating string within an enclosed space. The person is looking for a reference or advice on how to calculate the energy distribution at a specific point between two fixed points on the string. A resource for such equations can be found at the provided link.
slcoleman
I'm looking for an equation and I am not quite sure where to start, and am hoping someone could direct me to a good reference to some similar type equations, or at least kick me over to the proper forum.

I am looking for an equation that describes the energy distribution within the space containing a vibrating string. Think of it as being an enclosed evacuated box with a rubber band or piano wire connected to each end, and is vibrating at the primary frequency. I can guess that the length, deflection distance, width, elasticity, and density of the band would all come into play, and no doubt several other parameters which I have not yet thought of.

I am sure there are basic wave mechanical equations for vibrating strings vs frequency and length in all the standard textbooks, but can anyone offer me advise on how to get an energy distribution at point L between two fixed points from this vibrating string scenario?

Steve.

## 1. What is energy density distribution?

Energy density distribution refers to the measure of energy per unit volume or unit mass in a given system. In the case of a vibrating string, it represents the distribution of energy along the length of the string.

## 2. How is energy density distribution calculated?

The energy density distribution of a vibrating string can be calculated using the formula: u = 1/2 ρω^2A^2 sin^2(kx - ωt), where ρ is the linear mass density of the string, ω is the angular frequency, A is the amplitude of the string, k is the wave number, x is the position along the string, and t is time.

## 3. How does energy density distribution affect the vibration of a string?

The energy density distribution affects the amplitude and frequency of the vibrations in a string. Areas with higher energy density will have greater amplitude and lower frequency, while areas with lower energy density will have smaller amplitude and higher frequency.

## 4. What factors can influence the energy density distribution of a vibrating string?

The energy density distribution of a vibrating string can be influenced by various factors such as the tension, length, and density of the string, as well as the frequency and amplitude of the vibrations.

## 5. How is energy conserved in a vibrating string?

Energy is conserved in a vibrating string through the transfer of energy between different parts of the string. As the string vibrates, energy is constantly being transferred from areas with high energy density to areas with low energy density, ensuring that the total energy of the system remains constant.

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