Resonance

Resonance is a phenomenon in which a system exhibits a disproportionately large response to a driving force at a particular frequency. It occurs when the driving frequency matches or is close to a natural frequency of the system, which depends on properties such as mass and stiffness. Damping, energy losses, and how energy is supplied influence both the height and the width of the resonance peak.

In mechanical and electrical systems, resonance leads to large oscillations and high energy transfer. In a simple damped driven harmonic oscillator, the natural frequency is ω0 = sqrt(k/m). Without damping, driving at ω0 can cause unbounded growth; with damping, the maximum response occurs near ω0, and the peak is finite. The quality factor, Q, measures how sharp the resonance is; low damping broadens the peak, while high damping narrows it.

Common examples include vibrating musical instruments, where driving near a string’s natural frequency produces loud tones; a wine glass can resonate and possibly shatter when exposed to a suitable tone; and electrical LC circuits exhibit resonance when inductive and capacitive reactances cancel. Acoustic resonance occurs in cavities and tubes, shaping the distribution of sound in rooms and instruments.

In chemistry, resonance describes the delocalization of electrons in certain molecules, represented by multiple contributing structures; the actual electronic structure is a hybrid of these Resonance structures rather than any single one.

Resonance can be useful for selective amplification and sensing, but it can also be hazardous, causing fatigue or failure in structures and machinery if not properly controlled.