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lecture05 - 9 Two-mass vibrator Longitudinal vibration m m...

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9. Two-mass vibrator m m m m m k f a π 2 1 = m k f a 3 2 1 π = Longitudinal vibration Modes (a) and (b) are independent Transverse vibration m m m m Two-mass vibrator has 2 longitudinal and 4 transverse modes of vibration Violin string normally vibrates transversely
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10. Systems with many modes N-mass 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 mass-spring 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 ϖ ϖ φ ϖ sin cos cos ) ( + = + = = n n tot t x t x ) ( ) (
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Standing waves on a string Vibrating string can be thought of as the limit of the mass-spring system when the number of masses becomes very large
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1. There are many examples of waves: - Seismic waves - Ripples on a pond - Sound
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