# Standing Wave Fundamental Frequency and Particle Vibration

For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) travelling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the standing waves in the medium/string. Is this totally different from the frequency of the individual particles in the medium which execute an SHM with a fixed amplitude, calculated out of ω . What is the physical difference of frequency that maybe calculated from ω and the natural frequencies ?

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sophiecentaur
Gold Member
. Is this totally different from the frequency of the individual particles in the medium which execute an SHM
It's the geometry / dimensions of the whole oscillating system that determines the resonance and not the individual particles. The particles are not associated with any particular frequency - they will have a whole range of speeds and collision rates and can be changing direction, individually in a random way due to collisions. They cannot 'know' about the oscillations - they can only move in the direction that the instantaneous pressure is pushing them in bulk. But the temperature in a gas (aka average Energy of particles) can affect the bulk properties of the medium (wave speed).

Nikhil Rajagopalan
The particles themselves don't have any frequency associated. So you cannot say that the standing wave frequency is different from the frequency of the particles. A particle attached to a spring (like in the simple harmonic oscillator) oscillates with a specific frequency. The same particle attached to a different spring oscillates with a different "natural frequency". So the frequency is associated with the particle in a specific elastic potential.

If you have multiple particles interacting by elastic forces there are multiple natural (or normal modes) frequencies associated with the system, like in the waves on a string. So there is nothing to compare. The isolated "particles" don't have frequencies.

sophiecentaur