(a) Speed of sound in air 332 m/s at NTP. What will the speed of sound in hydrogen at NTP if the density of hydrogen at NTP is (1/16) that of air.
(b) Calculate the ratio of the speed of sound in neon to that in water vapour any temperature. [Molecular weight if neon `= 2,02 xx 10^(-2) kg//mol` and for water vapours `= 1.8 xx 10^(-2) kg//mol` ]

Explanation

The velocity of sound in air is given by `= sqrt((E)/(rho))=sqrt((gamma P)/(rho))=sqrt((gamma RT)/(M))`
(a) In terms density and pressure
`(V_(H))/(V_("air"))=sqrt((P_(H))/(rho_(H))xx(rho_("air"))/(P_("air")))=sqrt((rho_("air"))/(rho_(H)))["as" P_("air")=P_(H)] rArr V_(H)=V_("air")xxsqrt((rho_("air"))/(rho_(H)))=332xxsqrt((16)/(1))=1328 m//s`
(b) In terms of temperature and molecular weight `(V_(Ne))/(V_(W))=sqrt((gamma_(Ne))/(M_(Ne))xx(M_(W))/(gamma_(W)))["as" T_(N)=T_(W)]`
Now as neon is mono atomic `(gamma = 5//3)` while water vapours poly atomic `(gamma = 4//3)` so
`(V_(Ne))/(V_(W))=sqrt(((5//3)xx1.8xx10^(-2))/((4//3)xx2.02xx10^(-2)))=sqrt((5)/(4)xx(1.8)/(2.02))=1.055`