# Number of modes in Cubic Cavity

• Keiner Nichts
In summary, the number of modes in a cavity is N1-N2, and the average energy for each mode is either k*T or hν/e^(hν/kT)-1.
Keiner Nichts

## Homework Statement

Calculate the number of modes in a cubic cavity of length a=2.5 cm in the wavelength interval (λ1,λ2) where λ1=500 nm and λ2=501 nm. What's the total energy which radiates from the cavity if it's kept at a constant temperature of T=1500 K.

## Homework Equations

I imagine these would be rather relevant: Number of modes in a cavity N= (8π/3)*(a/λ)^3 and the average energy for each mode which would be either k*T if we work with Rayleigh-Jeans or hν/e^(hν/kT)-1 if we work with Planck's derivation.

## The Attempt at a Solution

I thought of simply finding the number of modes as N1-N2 where N1 is the number for λ1 and N2 for λ2, and then multiplying by the average energy (Which, could someone please double-check that formula? I might have misinterpreted it as average energy of a mode and it might be something different.) Of course, if we use Planck's formula I would find the frequency as being c/λ so no biggie there. I just want to know if it's the correct way to go about it.

Keiner Nichts said:

## Homework Statement

Calculate the number of modes in a cubic cavity of length a=2.5 cm in the wavelength interval (λ1,λ2) where λ1=500 nm and λ2=501 nm. What's the total energy which radiates from the cavity if it's kept at a constant temperature of T=1500 K.

## Homework Equations

I imagine these would be rather relevant: Number of modes in a cavity N= (8π/3)*(a/λ)^3 and the average energy for each mode which would be either k*T if we work with Rayleigh-Jeans or hν/e^(hν/kT)-1 if we work with Planck's derivation.

## The Attempt at a Solution

I thought of simply finding the number of modes as N1-N2 where N1 is the number for λ1 and N2 for λ2, and then multiplying by the average energy (Which, could someone please double-check that formula? I might have misinterpreted it as average energy of a mode and it might be something different.) Of course, if we use Planck's formula I would find the frequency as being c/λ so no biggie there. I just want to know if it's the correct way to go about it.
Your formula are correct. And yes you may calculate N1-N2 that way. In this case, since the difference of wavelength is small compared to the wavelengths themselves, one could also take the derivative to find dN in terms of ##d \lambda## and use that to get dN directly.

Keiner Nichts
Thank you! As for the radiant energy, would mere multiplication with N give me the right answer? I see no reason why it should not, just making sure.

## 1. What is a cubic cavity?

A cubic cavity is a three-dimensional enclosed space that is typically shaped like a cube. It can be made out of a variety of materials, such as metal, glass, or plastic, and is often used in scientific experiments as a way to contain and manipulate light or other electromagnetic waves.

## 2. How many modes can a cubic cavity support?

The number of modes that a cubic cavity can support depends on its size and shape. In general, a cubic cavity can support up to three different modes, also known as resonances, which correspond to the three axes of the cube. These modes are often referred to as the x, y, and z modes.

## 3. How is the number of modes in a cubic cavity calculated?

The number of modes in a cubic cavity can be calculated using a formula known as the spherical wave expansion. This formula takes into account the size and shape of the cavity, as well as the wavelength of the light or electromagnetic waves being used. It is a complex mathematical calculation that requires knowledge of advanced calculus and physics.

## 4. Why is the number of modes in a cubic cavity important?

The number of modes in a cubic cavity is important because it affects the behavior of light or electromagnetic waves inside the cavity. Different modes have different frequencies and patterns, which can be manipulated to achieve different outcomes. For example, the number of modes can determine the polarization of light or the direction of propagation.

## 5. Can the number of modes in a cubic cavity be changed?

Yes, the number of modes in a cubic cavity can be changed by altering its size, shape, or the material it is made of. Additionally, by introducing certain materials or structures inside the cavity, the number of modes can also be manipulated. This allows scientists to control and customize the behavior of light or electromagnetic waves in the cavity for various applications.

Replies
2
Views
2K
Replies
3
Views
1K
Replies
6
Views
1K
Replies
5
Views
3K
Replies
3
Views
1K
Replies
14
Views
2K
Replies
5
Views
2K
Replies
10
Views
7K
Replies
1
Views
4K
Replies
1
Views
2K