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Use the formula v= sqrt((gamma p)/(rho)) to explain why the speed of sound in air (a) is independent of pressure. (b) increases with temperature. (c ) increases with humidity |
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Answer» Solution :Assume ideal gas law `p = (rho RT)/(M)`, where `rho` is the density, M is the molecular mass, and T is the temperature of the gas. This gives `v= sqrt((gamma RT)/(M))`. This shows that v is : (a) Independent of pressure (b) INCREASES as `sqrtT` (c ) The molecular mass of WATER (18) is less than that of `N_(2) (28) and O_(2) (32)` Therefore as humidity increases, the effective molecular mass of air DECREASES and hence v increases. |
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