# The speed of sound in air at 15 c and 76 cm of Hg is 340m/sec. The speed of sound in air at 30c and 75 cm of Hg will be

1
by rahussain

2015-04-01T16:48:56+05:30

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Speed of sound in air at the temperature of 15 °C and the pressure of 76 cm of Hg
= 340 meters/sec.
Speed of sound at 30 °C and 75 cm of Hg = ?

Velocity of sound in air is proportional to square root of absolute temperature.
v   α  √T      ,  where T = absolute temperature of air
v at 30 °C / v at 15°C  =  √(273.15 + 30) / √(273.15 + 15)
v at 30 °C  = 340 m/s * √303.15/√288.15
=  348.74 m/sec  approx.

Velocity of sound waves in ideal gases do not depend on pressure or density.  It depends only on the temperature.  The effect due to pressure is cancelled exactly by the effect due to density.

v = √(γ R T / M) = √ (γ P / ρ)
γ = 1.4 approx = ratio of specific heats
R = universal gas constant
M = molar mass
ρ = density
P = pressure.
Since, we have  P/ρ in the formula,  the effect of changes in pressure and density cancel.  Low pressure gives rise to low density, for example.