- #1
mbigras
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Homework Statement
a) Find the frequency of vibration under adiabatic conditions of a column of gas confined to a cylindrical tube, closed at one end, with a well-fitting but freely moving piston of mass m.
b) A steel ball of diameter 2 cm oscillates vertically in a precision-bore glass tube mounted on a 12-liter flask containing air at atomospheric pressure. Verify that the period of oscillation should be about 1 sec. (Assume adiabatic pressure change with [itex]\gamma[/itex] = 1.4, Density of steel = 7600 [itex]\frac{kg}{m^{3}}[/itex]
Homework Equations
from part a, we get:
[tex]\omega = \left( \frac{\gamma p A}{m l} \right) ^{1/2}[/tex]
where [itex]p[/itex] is the pressure, [itex]A[/itex] is the area of the tube, [itex]l[/itex] is the length from the bottom of the tube to an undisplaced piston.
for part b, I thought it would be realistic to state the period as:
[tex]T = 2*pi \left( \frac{m l}{A \gamma p} \right) ^{1/2}[/tex]
before going on I suspect this may be where I'm getting hung up. I'm assuming the 12 L flask to be equivalent to a tube that is the area of the steel ball and then a given length so both volumes match. Also I'm assuming the steel ball to be about the same as a piston, only really taking into account its sphericalness when calculating the mass from the density of steel and the volume of a sphere.
[tex]l = \frac{V}{A}[/tex]
Are these two assumptions realistic?