C.4 Standing Waves and Resonance

Antinodes

The point of a standing wave where amplitude of oscillation is at a maximum.

Nodes

A point of a standing wave where amplitude of oscillation is zero.

Boundary Conditions

The conditions at the ends of a string or pipe. For a string, an end can be fixed or free. For a pipe, an end can be open or closed.

Equations for wavelength open-open

2L/n

Equations for wavelength open-closed

4L/n(odd)

Resonance

When the frequency of the energy incident on a system is equal to that of the system’s natural frequency, it vibrates at maximum amplitude.

Natural Frequency

The frequency at which a system vibrates or oscillates when it is disturbed.

Driving Frequency

The frequency of the oscillator supplying energy to the system.

Resonant Frequency

The frequency at which the oscillations of an object gain the greatest amplitude.

Damping

Techniques used to restrain and reduce oscillations and vibrations.

Light Damping

A system continues to oscillate and the amplitude of the oscillations decreases exponentially over time.

Heavy Damping

When a system dissipates all its energy without oscillating. It returns at a slow rate to its equilibrium position.

Critical Damping

The system returns to its equilibrium state as quickly as possible, without oscillating.