Course:PHYS341/2018/Calendar/Lecture06

Phys341 Lecture 06: Summary and web references

2018.01.15

Textbook: 6.1-6.5

Lecture 6: Resonance and Beats

1. Resonance
   • In plain language, if you hear a comment that resonates with you, that implies you share some quality with the speaker, and the comment produces a bigger reaction in you than in others who do not share that quality.
   • Ditto in vibrating systems
   • Possess natural (resonant) vibration frequencies
   • Can be excited into motion more easily by a source vibrating at the same frequency
   • “Natural” and “resonant” frequency often used interchangeably.
2. Sympathetic strings
3. Coupled pendula
4. Resonance curve
   • Graph shows vibration amplitude a of a mass on a spring, driven by a force with varying frequency f.
5. Cavity (“Helmholtz”) resonators
   • Beer bottles and ocarinas
6. Acoustic filters
7. Helmholtz resonators have been used to adjust acoustic response and noise output in:
   • Concert halls
   • Exhaust pipes
   • Jet engines
8. Beats
   • Two tones far apart will either sound as separate tones or merge together into a complex tone
   • Two tones too close together to sound different, but not identical will:
   • Sound as one for a short while but:
   • Periodically the pressure waves will get out of step and cancel each other out
   • This beating is occurs regularly with a frequency equal to the difference of the two frequencies contributing
   • e.g. tuning a string bowed string instrument (more later), twin-engined aircraft with engines not quite going the same speed (often heard above the skies of Vancouver)
9. Beats demonstration
   • Two demonstrate on a computer open http://www.szynalski.com/tone-generator/ in two windows and see how the two tones interact with each other.