Standing Waves and Resonant Frequencies

Resonant Frequencies

• A resonant frequency (natural frequency) is the frequency at which a standing wave can exist in a medium.
• Some objects have a single resonant frequency (e.g., tuning fork, pendulum); others have multiple (e.g., rope, air column).
• For objects with multiple resonant frequencies, each frequency is a whole-number multiple of the lowest resonant frequency, called the fundamental frequency (f_0).
• Waves with frequencies equal to the resonant frequencies of the medium will persist.

Standing Waves in a String (Fixed Ends)

• Nodes must occur at the fixed ends of a vibrating string.
• The fundamental frequency / first harmonic is the lowest frequency at which a standing wave is produced.
• At the fundamental frequency, the distance between the two fixed ends is equal to one half a wavelength (L = \frac{\lambda}{2}).
• This configuration has only one loop or antinode.