The correct option is D vo√7
At a given pressure and temperature, the density of gas is directly proportional to its molecular weight.
PM=ρRT
⇒ρ∝M
⇒ρ1ρ2=M1M2=232=116
⇒ρ2=16ρ1 ...............(1)
Here,
ρ1→ density of hydrogen,
ρ2→ density of oxygen
Now, density of mixture,
ρmix=ρ1 V1 +ρ2 V2V1+V2
⇒ρmix=ρ1V1+16ρ1×2V13V1+2V13=35ρ1 V15V1
[ given V1V2=32 and from (1)]
⇒ρmix=7 ρ1 ..........(2)
Speed of sound,
v=√γPρ
At constant pressure,
v∝1√ρ
So,
vH2vmix=√ρmixρH2
⇒vmix=vH2×√ρH2ρmix
⇒vmix=vo×√ρ17ρ1
⇒vmix=vo√7