Oxygen is `16` times heavier than hydrogen. At `NTP` equal volumn of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

Options

A. `sqrt(8)`
B. `sqrt((1)/(8))`
C. `sqrt((2)/(17))`
D. `sqrt((32)/(17))`

Answer

C

Explanation

Number of modes prop volume
`M= (n_(1)M_(o_2) + n_(2) M_(H_2))/(n_(1) + n_(2))`
= `((1) (32) + (1)(2))/(2) = 17`
Now, `nu = sqrt((gamma RT) / (M)) prop (1)/ sqrt(M)`
`nu_(1)/ nu_(2) = sqrt((M_(2))/ (M_(1))) = sqrt((2) / (17))`