- #1
sawer
- 65
- 2
Are these two, wave number and wave mode, same thing?
If not, what is the difference?
Thanks...
If not, what is the difference?
Thanks...
WannabeNewton said:Each mode of the electromagnetic field of the radiation in the cavity has an energy ##k_B T## by application of the equipartition theorem to the electromagnetic energy density.
sawer said:So if we rewrite this sentence: each "antinode" of a standing wave has an energy of ##k_B T## . Right?
WannabeNewton said:No. Each mode has an energy ##k_B T## from the equipartition theorem. A mode is not the same thing as a node or antinode.
sawer said:If a standing wave has 3 antinodes and we say its mode number is 3. So why is mode not the same thing as antinode?
sawer said:Here it says: "number of modes" per unit frequency per unit volume.
sawer said:For the first picture: there are 3 standing waves and 5 waves. Now which number is the number of modes? 3 or 5?
WannabeNewton said:Yes the number of antinodes of the standing wave is the same as the mode number but a mode itself refers to one of the independent harmonic oscillator solutions
WannabeNewton said:Which picture exactly?
sawer said:So wave mode refers to one particular frequency of a standing wave and wave number is the number of antinodes of that wave. So wave mode number indicates wave numbers but mode itself indicates frequency. Right? There are many different frequencies of waves(different wave modes), but, one type of mode indicates one frequency. Right?
sawer said:What does "more modes" mean? Doesn't one frequency indicate one mode?
sawer said:"For higher frequencies you can fit more high frequency of wave into the cavity"
It doesn't make sense.
sawer said:So I began to think for wave mode as a number of antinodes, not as a standing wave of a particular frequency.
sawer said:What does that mean: "For higher frequencies you can fit more modes into the cavity".
Ah OK.sawer said:Yes I checked.
Linear wave number is L/(λ/2) for a specific frequency. That gives antinode number in a standing wave. So these two must be same thing.
Wavenumber is a unit of measurement used to describe the spatial frequency of a wave. It is defined as the number of wave cycles per unit distance, typically measured in inverse meters (m^-1) or inverse centimeters (cm^-1).
Wavenumber and wavelength are inversely proportional to each other. As wavenumber increases, wavelength decreases, and vice versa. This means that waves with a shorter wavelength have a higher wavenumber and vice versa.
While wavenumber measures the spatial frequency of a wave, frequency measures the temporal frequency of a wave. Frequency is defined as the number of wave cycles per unit time, typically measured in Hertz (Hz) or cycles per second (s^-1).
Wavenumber is often used in spectroscopy because it is a more convenient unit for measuring the energy levels of molecules. This is because the energy of a photon is directly proportional to its frequency, and since wavenumber and frequency are inversely proportional, wavenumber is also directly proportional to energy.
Wavenumber and wave mode are both characteristics used to describe a specific type of wave. Wavenumber describes the spatial frequency, while wave mode describes the pattern or shape of the wave. For example, a wave with a high wavenumber and a sinusoidal wave mode would have a high frequency and a smooth, oscillating pattern.