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No. If a vibration is smaller, the sound is higher pitched. To get a quieter sound the amplitude of the sound-wave needs to be smaller.

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It depends whether you mean amplitude or wavelength being "smaller", and they are two different things. If the vibration's amplitude is smaller the sound is quieter irrespective of frequency. If the vibration is more rapid, the frequency is higher but the wavelength correspondingly smaller irrespective of amplitude.

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Q: Is a sound quieter when a vibration is smaller?
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