Lecture 31 - Forced Oscillations - Normal Modes - Resonance - Natural Frequencies - Musical Instruments
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1. Forced Oscillations:
When applying an external sinusoidal force (a driving force), to a spring system, there will be a transient response in addition to a steady state response. When the transient response has died (due to friction), the steady state remains. Resonance responses are described.
2. Resonances and Normal Modes:
Systems of coupled oscillators with multiple resonant frequencies are described, including a violin string. Normal modes of an oscillating string occur at integral multiples (harmonics) of the fundamental; these natural frequencies are determined by the length, the tension, and the mass per unit length of the string.
3. Resonance in Wind Instruments:
Air pressure waves in boxes, cavities, and hollow tubes exhibit a series of resonances determined by the velocity of sound in air and the dimensions of the systems. The frequency of these resonances can be altered by holes or pistons to change their effective size. Professor Lewin demonstrates this with a wooden flute and he plays Jingle Bells on a wooden trombone.
4. Nonlinear Response at Resonance:
Excitation with a spectrum of frequencies often reveals some resonant frequencies as the object responds most strongly to those frequencies. Resonance can be destructive if the driving force is strong enough, as dramatically shown with a wine glass driven by strong sound waves, and the Tacoma Narrows bridge driven by the wind.
5. Speed of Sound in a Resonant Cavity:
Each person's distinctive voice is produced in a manner similar to the way sounds are produced by wind instruments. If these instruments were filled with helium instead of air, the frequencies of the sound would be very different as the speed of sound in helium is substantially larger than that in air. Professor Lewin inhales helium to demonstrate this. His familiar voice cannot be recognized anymore.
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