Every oscillating system has a natural frequency () — the frequency at which it oscillates freely when displaced and released. When an external periodic driving force is applied at exactly this natural frequency, the system absorbs energy most efficiently and the amplitude of oscillation builds up to a maximum. This phenomenon is called resonance.
Resonance occurs when the frequency of the applied driving force equals the natural frequency of the system, resulting in maximum amplitude of oscillation.
At resonance:
The sharpness of a resonance peak describes how rapidly the amplitude falls off as the driving frequency moves away from .
| Factor | Effect on Resonance Peak |
|---|---|
| Low damping | Sharp, tall, narrow peak — high amplitude at |
| High damping | Broad, flat, short peak — lower amplitude at |
The quality factor (Q-factor) is a qualitative measure of sharpness:
1. Radio Tuning A radio receiver contains an LC circuit whose natural frequency can be adjusted (by varying capacitance). When the circuit's natural frequency matches the frequency of a broadcast signal, resonance occurs and that station's signal is amplified to maximum amplitude. Other stations at different frequencies produce little response. This is how a radio tunes in to a specific station.
2. Microwave Ovens Microwaves are tuned to the natural frequency of water molecules, causing them to resonate and absorb energy efficiently — heating food.
3. Musical Instruments Strings, air columns, and resonating chambers are designed so that resonance amplifies specific frequencies to produce musical notes.
1. Bridges (Tacoma Narrows, 1940) The Tacoma Narrows Bridge in Washington, USA collapsed in 1940. Wind created periodic vortices that matched the bridge's natural frequency, driving it into resonance. The amplitude of oscillation grew until the bridge tore apart. Modern bridges are designed with damping mechanisms and aerodynamic shapes to avoid resonance.
2. Buildings in Earthquakes If the frequency of seismic waves matches the natural frequency of a building, resonance can cause catastrophic structural failure. Engineers design buildings with natural frequencies far from typical earthquake frequencies.
3. Aircraft Engines Engine vibrations must not match the natural frequency of the aircraft's wings or fuselage, as resonance could cause structural failure.
| Situation | Resonance Effect | Desired Outcome |
|---|---|---|
| Radio tuning | Maximum signal amplitude at | Useful — select one station |
| Bridge in wind | Growing oscillation amplitude | Dangerous — must be avoided |
| Microwave oven | Maximum energy absorption by water | Useful — efficient heating |
| Car suspension | Road vibrations at natural frequency | Dangerous — critical damping used |