The speed of sound in air at 15^oC and 76 cm of Hg is 340 m/s. The speed of sound in air at 30^oC and 75 cm of Hg will be (in m/s)

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340 $\sqrt{2}$

340 $\sqrt{\frac{2 x 75}{76}}$

340 $\sqrt{\frac{303}{288}}$

340 $\sqrt{\frac{288}{303}}$

answer is A.

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Detailed Solution

T₁ = t + 273 = 15 + 273 = 283k
T₂ = 30 + 273 = 303k
V₁ = 340 m/s $V \propto \sqrt{T}$
$\frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow V_{2} = V_{1} \sqrt{\frac{T_{2}}{T_{1}}}; V_{2} = 340 \sqrt{\frac{303}{288}}$

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