A common lecture demonstration is as follows: hold or clamp a one meter long thin aluminium bar at the center, strike one end longitudinally (i.e. parallel to the axis of the bar) with a hammer, and the result is a sound wave of frequency 2500 Hz.
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The point where the bar is struck is an antinode and the point where it is held a node. With the bar held at the center and its one end struck, the wavelength 
is related to its length L by 
. Hence the speed of sound propagation in the aluminium bar is
The speed of sound in a solid is
where Y is the Young's modulus of its material and 
its density. The speed of sound in a fluid is
where M is its bulk modulus and 
its density. For adiabatic compression of a gas, 
, where p is its pressure and 
the ratio of its principal specific heats; 
for air, a diatomic gas. Hence
With
.
Suppose the bar is held at distance x from the struck end. We have
Hence the bar is to be held at 
from the struck end. If it is so held but struck at the other end, we would have
and the frequency would become 1875 Hz .
If the bar is struck transversely, the wave generated will be transverse, not compressional, and the velocity of propagation is then given by
where N is the shear modulus. As the shear modulus of a solid is generally smaller than its bulk modulus, v is now smaller. And as
the frequency generated is lower.
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