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When we tear a dry paper, it produces a clear audible sound but when the same experiment is tried with a wet paper, we hardly hear any sound.

So can someone explain me what is happening here at the atomic scale ? Why isn't the wet paper creating any sound at all ?

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    $\begingroup$ "atomic scale" probably is too small. The stuff we call "paper" is a mat of tangled fibers that are somewhat glued together. Part of the answer to your question will hinge on how the fibers interact with each other and with the "glue" when the paper is wet vs. when it is dry. I'm guessing that the water somewhat dissolves/softens the "glue," and it lubricates the fibers. $\endgroup$ Nov 24, 2020 at 17:38
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    $\begingroup$ The other part of your question will depend on how sound propagates through wet vs. dry paper, and how well the paper is able to couple that sound to the surrounding air. Again, the "atomic scale" probably will be too small. Whatever the answer turns out to be, I bet it will be at the scale of the fibers, or even larger than that. $\endgroup$ Nov 24, 2020 at 17:40
  • $\begingroup$ Cause they don't feel like it. $\endgroup$ Mar 4, 2021 at 19:54

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Sound is just mechanical vibration. There are two reasons why tearing wet paper is a poor source

The lower strength of wet paper means that less energy is needed to tear the fibres apart. That means less is available to turn into sound.

Wet paper is soggier than dry, meaning it is more squashy and absorbs small movements. This means that any small movement of fibres due to tearing will simply get absorbed and the mechanical rebound, which would create the sound, does not happen.

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    $\begingroup$ what did you mean by mechanical rebound ? $\endgroup$
    – Ankit
    Nov 25, 2020 at 2:52
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    $\begingroup$ @Ankit When you stress an elastic material a little, it will deform slightly. But stress it so much that it tears, and the deformed edges then snap back, or rebound, into place. Dry paper can stretch that little bit, wet paper is too weak and simply falls apart. $\endgroup$ Nov 25, 2020 at 9:02
  • $\begingroup$ The mechanical rebound is also amplified by the paper itself, which acts as a large surface for the creation of sound waves. Water dampens this effect (literally). $\endgroup$ Feb 27, 2021 at 15:35
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I have a couple of thoughts on this question, and though I admit they are speculations, I hope they are educated ones!

Paper is an interesting material. As to what exactly paper is, Wikipedia tells us that:

Paper is a thin sheet material produced by mechanically and/or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed on the surface, followed by pressing and drying.

What holds the fibers together? This is a very interesting question as we still don't have a complete picture of the forces holding these fibers together as this recent (2013) paper paper tells us:

Several mechanisms have been suggested to play a significant role in forming the fibre-fibre bonds that lead to the fibre network that we call paper. In the past, the following possible bonding mechanisms were considered: hydrogen bonds, mechanical interlocking, electrostatic interactions, interdiffusion of cellulose molecules and van der Waals forces. More recently, microcompressions, capillary bridges and stress due to the drying process have been under discussion. What is agreed is that all of these mechanisms contribute in some way to bonding two pulp fibres together. It is still not clear, however, which of these mechanisms dominates or if an interplay of several mechanisms is relevant.

Now, as other folks who have posted answers to this question correctly note, sound is a vibration. When you tear paper, you are breaking the bonding mechanism that holds the fibers together. As you begin to tear, these bonding mechanisms resist and the fibers, on a microscopic scale near where you are trying to tear, get stretched apart from one another as if they were attached to little springs.

Once you actually make a tear, the fibers on either side of the tear rebound backwards because of this spring force and that creates vibrations in the air.

Now when paper is made wet, water, being a polar molecule, finds it easy to insert itself between fibers, since cellulose is also polar. The image below from this link, gives a visual of this:

enter image description here

We must assume there that the insertion of a water molecule, in addition to pushing the fibers further from each other, significantly weakens the "spring constant" between fibers.

I would imagine that this has two effects:

1 - The stretching between fibers is much less when tearing wet paper that dry and this, in turn, reduces the amplitude of the pressure vibrations in the air (sound), and

2 - The water molecule acts as a damping mechanism, or cushion, further reducing the air pressure vibrations that occur during a tear.

The connection between the mechanical vibrations and the air pressure vibrations is, I suspect, also two-fold:

1 -Obviously, the vibrations of the fibers which strike air molecules.

2 - When the fibers are stretched some air molecules probably move slightly into some of the surface interstices between the fibers for a few layers. When the fibers snap back after the tear starts, these air molecules are pushed back out, thereby striking other air molecules.

The strength of the response of the air in both of these mechanisms to the tear will be affected by the strength of the mechanical response of the fibers during tearing.

Finally, I would also point out, though it must be obvious at this point, that the question is somewhat flawed. Wet paper DOES make a sound on tearing. It is just that this sound is much softer than dry paper.

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  • $\begingroup$ thanks for this answer (+1) .. but how will you support your statement that We must assume there that the insertion of a water molecule, in addition to pushing the fibers further from each other ? $\endgroup$
    – Ankit
    Feb 27, 2021 at 17:17
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    $\begingroup$ Hi @AStudent4ever . Thanks for the question. I am making this assumption based upon my knowledge of polymeric materials and substances we call 'plasticizers'. A plasticizer can be water or some other solvent, that is typically added to a polymer to lower its glass transition. While the theory can be complex, it is thought that in increase in the free volume, by the solvent pushing the polymer chains apart, is one result of adding a plasticizer. And cellulose is a polymer. See "Fox Equation" section of this Wikipedia article: en.wikipedia.org/wiki/Flory%E2%80%93Fox_equation $\endgroup$
    – CGS
    Feb 27, 2021 at 18:00
  • $\begingroup$ so does water molecules limit the vibrational time period too alongwith the amplitude ? $\endgroup$
    – Ankit
    Mar 3, 2021 at 6:06
  • $\begingroup$ Hi @AStudent4ever . We would expect that tearing a paper acts as a short impulse. Any model of dry paper would include a damping term, that, in response to the paper being torn, would result in damped vibration of the paper molecules. Adding water modifies the damping term. We assume the system is underdamped since we do get sound in either case. In an underdamped harmonic oscillator the natural frequency is modified by the damping term: $w_1=(w_0^2-y^2)^{0.5}$, where $w_0$ is the natural frequency and y is proportional to the damping. Increasing y will result in an increased period. $\endgroup$
    – CGS
    Mar 4, 2021 at 0:12
  • $\begingroup$ so does water molecules increase or decrease the period of vibration ? $\endgroup$
    – Ankit
    Mar 4, 2021 at 6:38
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This is just because of the damping in the molecules of paper. Generally, if you take a rope and wave it like a transverse wave, you would perfectly notice that after sometime, it stops. Why? Just because of damping.

In the same way, when you wet a paper, damping is increased to very high number. Thats why it suppresses the vibrations caused due to tearing of the paper, causing it to make no or negligible sound.

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The hydrogen bonds in cellulose is what gives paper its strength. When you try to tear a dry paper you have to apply a comparatively larger force to break these bonds. The breakage of the fine interlocked fibres in paper produces the sound. When the paper becomes wet, water gets absorbed into the paper. The high dielectric constant of water (80.4) decreases the force of the hydrogen bonds considerably (it becomes 1/80.4 times the initial strength). This reduces the extent of interlocking as well as the force between fibres.

For sound to be produced, we require some tension in these fibres. While dry paper creates enough tension before breaking, the fibres in the wet paper simply slide apart.

Thus tearing a wet paper becomes easier and produces almost no noise.

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