Standing waves and resonance and damping

standing wave is formed when

When two waves of the same speed, wavelength and amplitude travelling in opposite directions meet, a standing wave is formed. According to the principle of superposition, the resulting wave has a displacement that is the sum of the displacements of the two travelling waves.

damping

An oscillating system that is subject to frictional forces will lose energy, and the amplitude of oscillations will decrease; we have damping.

resonance

When these two frequencies are equal, we have resonance, and the system responds by showing oscillations with large amplitude.

nodes

There are some points on the string where, as a result of destructive interference between the two waves, the displacement is always zero. We call these points nodes. The distance between two consecutive nodes is half a wavelength.

antinodes

Half-way between nodes are points where, as a result of constructive interference, the displacement gets as large as possible. These points are called antinodes. Note that the nodes always have zero displacement whereas the antinodes are at maximum displacement for an instant of time only

for 2 closed or 2 open   

For one closed and one open  

natural frequency

We will now examine qualitatively the effect of an externally applied force F on a system that is free to oscillate with frequency f₀. This is called the natural frequency of the system.

driving frequency

The force F will be assumed to vary periodically with time with frequency f_d, called the driving frequency.

Light, critical and heavy damping