A pipe of length 1.5m closed at one end is filled with a gas and it resonates in its fundamental with a tuning fork. Another pipe of the same length bur open at both ends is filled with air and it also resonates in its fundamental with the same tuning fork. Calculate the velocity of sound at `0^(@)C` in the gas. Given that the velocity of sound in air is 360 m/s at `30^(@)C` where the experiment is performed.

Explanation

Let `V_(G) V_(A)` are velocities of sound in gas and air respectively. If f is the frequency of tuning fork then according to given problem at `30^(@)C`,
`f=f_(c) and f=f_(0), f_(c)= f_(0) or (V_(G))/(4L)=(V_(A))/(2L)`
I,.e `v_(G)=2v_(A)=2xx360=720 m//s`
Now as in case of sound `v prop sqrt(T)`
`:.(V_(g))_(0)=(V_(G))_(T) sqrt((273)/(303))=684m//s`