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I am mostly a mathematician but have some physics background. I was tutoring high school physics, and we were covering the speed of sound in various mediums. He noticed that the speed of sound in metal is greater than in water. He said if you hit metal, it's usually pretty loud where if you hit water, it's usually not as loud. "Hitting air" is usually silent and air has an incredibly low speed of sound. Is there a relationship between these two?

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    $\begingroup$ You're using a an imprecise measure (sound when "hitting" something) and in addition applying it to materials in widely different phases (gas, liquid, and solid). Despite that, there is sort of a weak relationship between "loudness of hitting"and sound velocity. Sound velocities increase with the bulk modulus of the material (longitudinal waves) or the shear modulus of the material (transverse waves), and materials with higher bulk or shear moduli will tend to make a bigger sound when hit under the same conditions (e.g., metal ball versus sponge ball). This is not very quantitative, though. $\endgroup$ – Samuel Weir Mar 12 '16 at 20:23
  • $\begingroup$ I am contacting you here to answer your question on the historic exposition or probabilistic path you deleted a while ago. I think it is a very important path to lead the students through history because it makes clear that it is the data that form theory, and not theory that forms the data. Physics is a discipline where obsrvations are fitted with mathematical models. This has to be ground into the concepts of physics students, particularly the one theoretically inclined, and this method does it. $\endgroup$ – anna v May 13 '16 at 5:23
  • $\begingroup$ see my answer to a naive question here physics.stackexchange.com/questions/193331/… . It is very important to get grounded on data. $\endgroup$ – anna v May 13 '16 at 5:27
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I think there is a potentially dangerous mixture of the principles:

  • speed of sound propagation is a feature of material (i.e. material related magnitude)
  • "loudness of the hit" strongly depends on a shape of a specific object (i.e. object related "magnitude")

Intensity of the radiated sound depends on magnitudes that might be related to speed of sound, but that may easily be a misleading clue. Hitting a metal coin and hitting a metal church bell is really not of the same loudness.

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The speed of sound depends upon the density of the material, and its stiffness. Obviously, a gas is not very stiff, nor is a marshmallow. OTOH, steel is quite stiff, and diamond is stiffer yet.

Some formulas and analysis are here.

The sound that your hand makes when striking something depends on many things, including the air trapped between your hand and the object; try clapping your hands with different curvatures of your hand. To eliminate that variation, try striking the various surfaces with different stiff objects, made of different materials. Your student would then be doing his own research, starting with the original hypothesis.

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To answer your question, no there is no relation between how loud of a sound an object produces and how fast sound travels in it.
Look at it like this, if you evaporate water you get steam which does not produce any Audible sound on hitting, but water does which is louder than the sound produced by same amount of ice when hit with same force (is what I think, still haven't found anything relevant to prove that) . But sound travels fastest in ice amongst the three.
When considering sound produced by hitting a metal object, you have to look into its harmonics the are responsible for many properties of the sound.

Hope that's helpful, I will add more as I learn more.

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