Final answer:
Resonant frequency is the natural vibration mode at which a system can oscillate with a large amplitude, seen in phenomena such as musical wind instruments, RLC series circuits, and mechanical oscillators like a paddle ball on a rubber band.
Step-by-step explanation:
The concept of resonant frequency is important in the study of oscillatory systems, such as those found in musical instruments, electrical circuits, and mechanical systems. In musical instruments that can be modeled as a tube with anti-symmetrical boundary conditions, such as wind instruments, resonant frequencies correspond to the natural vibration modes of the air column within the tube.
When excited at these frequencies, the system can oscillate with a large amplitude, leading to a phenomenon known as resonance.
An example of resonance in an electrical system is the resonant frequency of an RLC series circuit, where R represents resistance, L represents inductance, and C represents capacitance. At the resonant frequency, the impedance of the inductor and the capacitor cancel each other out, leading to the maximum power transfer to the circuit and a peak in amplitude of the oscillations.
The concept of resonant frequency also applies to physical systems, as demonstrated by the classic example of a paddle ball on a rubber band. When the system is driven at its natural frequency, it achieves resonance and the amplitude of oscillations increases dramatically. This effect is less pronounced when driving the system at frequencies higher or lower than the natural frequency, as energy transfer becomes less efficient.