# The speed of sound in oxygen  (O2) at a certain temperature is  460 ms-1 The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal) Option 1) Option 2) Option 3) Option 4)

Laplace formula (correct value )

$= \sqrt{\frac{\gamma P}{\rho }}$

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$\nu = \sqrt{\frac{\gamma P}{\rho }}= \sqrt{\frac{\gamma RT}{M}}$

$\gamma \: for\: O_{2}= 1+\frac{2}{5}=\frac{7}{5}$

$\gamma \: for\: H\! e= 1+\frac{2}{3}=\frac{5}{3}$

$\frac{\nu _{2}}{\nu _{1}}= \sqrt{\frac{\gamma _{He}}{4} \times \frac{32}{\gamma _{O_{2}}}}\times 460$$= \sqrt{\frac{5}{3}\times \frac{1}{4}\times \frac{32\times 5}{7}} \times 460=1420m/s$

$\nu = \sqrt{\frac{\gamma P}{\rho }}= \sqrt{\frac{\gamma RT}{M}}$

$\gamma \: for\: O_{2}= 1+2/5= 1.4$

$\gamma \: for\: H\! e= 1+2/3=5/3$

$\frac{\nu _{2}}{\nu _{1}}= \left ( \sqrt{\frac{\gamma _{He}}{4} \times \frac{32}{\gamma _{O_{2}}}}\right )\times 460$

$=460\times \sqrt{\frac{5}{3}\times \frac{1}{4}\times \frac{32\times 5}{7}}=1420m/s$

The value of the speed of sound in He should have been 965 m/s and that of O2 about 320 m/s. The value of the velocity given fo O2 is  quite high.

Option not given.

$V\:=\sqrt{\frac{\gamma P}{P}}\:=\:\sqrt{\frac{\gamma RT}{M}}$

$\gamma for O_{2}\:=\:1+\frac{2}{5}=\frac{7}{5}$

$\gamma for H_{e}=1+\frac{2}{3}=\frac{5}{3}$

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{\gamma H_{e}}{4}\times \frac{32}{\gamma O_{2}}}\:\times460\:\:\:\:=\sqrt{\frac{5}{3}\times\frac{1}{4}\times\frac{32\times 5}{7}}\:\times460\:=\:1420\:ms^{-1}$

Option 1)

Option 2)

Option 3)

Option 4)

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