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| Velocity of Sound in Gases (Newton's Formula) |
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| We know that the properties of a medium that govern the propagation of a mechanical wave are: |
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 a restoring force |
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 an inertial mass |
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| The restoring force acting on the particles of the medium is intimately connected to the approximate elastic modulus of the medium and the inertial mass, to its density. |
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| In 1676, Newton derived an expression for the velocity of sound in a homogenous medium. He showed that |
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 |
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| where v is the velocity of sound, E is
the modulus of elasticity and r is the density of the medium. When the medium is a gas only the bulk modulus is to be considered. |
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| Where B is the bulk modulus of elasticity. Newton assumed that the temperature remains constant when sound travels through a gas (air). Therefore the process is isothermal and Boyle's law can be applied. At a region of compression, the pressure increases and volume decreases. |
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| Let the initial pressure = P |
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| Initial volume = V |
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Increase in pressure =  P |
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Decrease in volume =  V |
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Then, final pressure = P +  P |
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Final volume = V -  V |
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Applying Boyle's law, (P +  P) (V - V) = PV |
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Expanding the terms, PV - P V + V P -  P. V = PV |
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Since the changes in pressure and volume are small,  P. V can be neglected. Then, |
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| Comparing equations (1-24) and (1-25), |
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| We get B = P |
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| Therefore, Newton's formula for velocity of sound can be written as |
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| At NTP., with pressure of air = P = 0.76 x 9.8 x 13.6 x 103 |
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| = 1.013 x 105 Pa or Nm-2 |
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| Substituting these values in equation (1-26) |
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| But this value of the velocity of sound at 0oC, is not in agreement with the experimental value which is 332ms-1. |
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