Natural Frequencies and Vibration Amplitudes of Object A

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When a complex sound wave strikes Object A, it vibrates at all frequencies, but non-natural frequencies diminish quickly compared to natural frequencies. The vibrations at natural frequencies are more vigorous, resulting in greater amplitude than those at other frequencies. This implies that Object A modifies the incident sound wave, producing a different complex sound wave. The discussion acknowledges the complexity of acoustics, suggesting that expert insights could further clarify these dynamics. Overall, the interaction between sound waves and Object A emphasizes the significance of natural frequencies in vibration response.
Tam Le
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Suppose a sound wave with multiple natural frequencies--a complex sound wave--strikes Object A. Some of those frequencies matches the natural frequencies of Object A.

A) Will Object A vibrate at all the different frequencies or only to its natural frequencies?

B) If Object A vibrates at all the different frequencies, does it vibrate more vigorously to its natural frequencies? In other words, will the amplitude of vibration of its natural frequencies be greater than the other frequencies?
 
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Tam Le said:
A) Will Object A vibrate at all the different frequencies or only to its natural frequencies?

I think it vibrates at all the frequencies, but the non-natural ones simply die off very quickly compared to the natural frequencies.

Tam Le said:
B) If Object A vibrates at all the different frequencies, does it vibrate more vigorously to its natural frequencies? In other words, will the amplitude of vibration of its natural frequencies be greater than the other frequencies?

I believe so. That would appear to match the explanation given at wiki: http://en.wikipedia.org/wiki/Natural_frequency
 
If that is true Drakkith, then wouldn't Object A produce a different complex sound wave compared to the incident complex sound wave? Thus, the sound wave I would hear from Object A would be a modified version of the incident sound wave.

Thank you for replying.
 
I'm not an expert in acoustics, but that sounds correct to me. I'm sure the details are pretty complicated though. Maybe someone with more experience in this area will chime in. (Hah! Chime in!)
 
I'm working through something and want to make sure I understand the physics. In a system with three wave components at 120° phase separation, the total energy calculation depends on how we treat them: If coherent (add amplitudes first, then square): E = (A₁ + A₂ + A₃)² = 0 If independent (square each, then add): E = A₁² + A₂² + A₃² = 3/2 = constant In three-phase electrical systems, we treat the phases as independent — total power is sum of individual powers. In light interference...

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