Speed of sound in an ideal gas is given by

#"v" = sqrt((gamma"RT")/"M")#

Where

- #gamma =#Adiabatic constant
- #"R ="# Ideal gas constant
- #"T ="# Absolute Temperature
- #"M ="# Molecular mass of gas

#underline(bb"Type of gas" color(white)(........) bb(gamma)color(white)(..))#

#"Monoatomic" color(white)(000=) 5/3#

#"Diatomic" color(white)(..............) 7/5#

#"Triatomic" color(white)(......!!!!!!) 4/3#

Nitrogen gas molecules are diatomic and that of Helium are monoatomic. So,

#"v"_("N"_2)/"v"_"He" = sqrt(gamma_("N"_2)/gamma_"He" × "M"_"He"/"M"_("N"_2))#

#color(white)("v"_("N"_2)/"v"_"He") = sqrt((7/5)/(5/3) × (4 cancel"g/mol")/(28 cancel"g/mol")#

#color(white)("v"_("N"_2)/"v"_"He") = sqrt(7/5 × 3/5 × 4/28)#

#color(white)("v"_("N"_2)/"v"_"He") = sqrt(cancel(7)/5 × 3/5 × (cancel(4))/(cancel(4) × cancel(7))#

#color(white)("v"_("N"_2)/"v"_"He") = sqrt(3)/5#