The time period of oscillations of an air bubble formed by an explosion inside water depends on the pressure (P), density (p), and energy due to explosion (E). The relationship between these factors can be established using the principles of fluid mechanics and the equations for pressure, density, and energy.
The pressure of a gas inside a bubble is related to its volume and temperature, and can be described by the Ideal Gas Law:
P = (nRT)/V
where n is the number of moles of gas, R is the gas constant, T is the temperature, and V is the volume of the gas.
The density of a fluid is related to its mass and volume, and can be described by the equation:
p = m/V
where m is the mass of the fluid and V is its volume.
The energy due to the explosion can be described by the equation:
E = (1/2)mv^2 + P_0V_0 - P_fV_f
where m is the mass of the gas, v is its velocity, P_0 and V_0 are its initial pressure and volume, and P_f and V_f are its final pressure and volume.
By combining these equations and using the principles of fluid mechanics, it is possible to establish a relationship between the time period of the oscillations (T), pressure (P), energy due to the explosion (E), and density (p). However, the exact relationship will depend on the specific conditions of the explosion and the fluid in which it occurs.
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