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Unformatted text preview: 9. Twomass vibrator m m m m m k f a 2 1 = m k f a 3 2 1 = Longitudinal vibration Modes (a) and (b) are independent Transverse vibration m m m m Twomass vibrator has 2 longitudinal and 4 transverse modes of vibration Violin string normally vibrates transversely 10. Systems with many modes Nmass vibrator has N longitudinal and 2N transverse modes of vibration 11. Vibrations in musical instruments 1. Strings 2. Membrane 3. Bar 4. Plate (Chladni patterns) 5. Tuning fork 12. Vibration Spectra (Fourier Analysis) Vibrating string can be thought of as the limit of the massspring system when the number of masses becomes very large (For the transverse vibrations see text book Fig. 2.12 ) ( 29 ( 29 ( 29 t b t a t A t x n n n n n n n n sin cos cos ) ( + = + = = n n tot t x t x ) ( ) ( Standing waves on a string Vibrating string can be thought of as the limit of the massspring system when the number of masses becomes very large 1. There are many examples of waves: Seismic waves Ripples on a pond...
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 Fall '09
 Mass

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