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According to our physics textbook, the source of sound is vibration. According to our chemistry textbook, substances in solid state have molecules vibrating in a fixed position. So why can't I hear my desk or something?

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    $\begingroup$ Because the frequency at which it vibrates air molecules is outside the range of human hearing or below the threshold amplitude. $\endgroup$ – Pieter Geerkens Oct 5 '13 at 4:55
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    $\begingroup$ And even if you could hear at that frequency, the sound of your own blood rushing through your ear would be louder than the sound of the molecules. $\endgroup$ – Pranav Hosangadi Oct 5 '13 at 5:47
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Good question, and there's some interesting physics in it.

As the comments have said, the frequency of vibration is way higher than your ears could detect. The frequency of thermal noise in a solid is around 10THz and the human ear can only hear sound up to around 20KHz.

However, even if you had super-hearing, you still couldn't hear your desk because there is an upper limit to the frequency of sound that can be transmitted through air of about 5Ghz. Have a look at Is there an upper frequency limit to ultrasound? as this gives an excellent description of the physics involved. The sound from your desk couldn't reach your ear as it's too high for the air to transmit.

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