Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. Ratio of their lengths respectively is

Options

A. `1:4`
B. `4:1`
C. `1:2`
D. `2:1`

Answer

A

Explanation

The fundamental frequency, `n=(v)/(4l)`
where, v=wave velocity
`(v_(H))/(v_(o))=(l_(H))/(l_(o))=(4)/(1)Rightarrow(v_(H))/(v_(o))=sqrt((M_2)/(M_1))=(v_(H))/(v_(o))=sqrt((32)/(2))=4`
Here, `M_(1) "and" M_(2)` are molecular weights of hydrogen and oxygen, respectively `v_(o):v_(H)=1:4`