46 2 Derivation of Acoustic Wave Equation
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γ ¼ 1:4 |
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J |
Kg m2 m |
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R ¼ 8:314 |
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¼ |
s |
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mol K |
mol K |
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T ¼ 15C ¼ 288:15K h Kg i mol
The speed of sound in air, pure oxygen, and pure nitrogen can be calculated using the same formula in this section. The speeds of sound in air, pure oxygen, and pure nitrogen are tabulated below:
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Molar mass (M ) |
g |
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Temperature(T |
|
Speed of sound |
m |
|
|
mol |
) [C] |
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|
|
s |
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Air |
28.95 |
15 |
|
340 |
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O2 (21% of air) |
31.999 |
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|
15 |
|
324 |
|
|
N2 (78% of air) |
28.013 |
|
|
15 |
|
346 |
|
|
Note that the ideal gas constant R is the same for all gases. The ratios of specific heats for N2, O2, and air are very close and are about 1.4. The ratios of specific heats could be different for different gases. For example, the ratio of specific heats for He is about 1.67.
2.5.4Formula Using Colliding Speed
The pressure due to one particle collision was derived in Sect. 2.3.2 as:
PoVa ¼ 13 mav2ca
Based on the equation above, the pressure for n moles of the particle is:
PV ¼ 13 nMv2ca
Substituting the equation above into the formulas for the speed of sound based on pressure gives:
r
c ¼ γPo
ρo