Two open organ pipes give 4 beats/sec when sounded together in their fundamental nodes. If the length of the pipe are 100 cm and 102.5 cm respectively, then the velocity of sound is :

Options

A. `160` m/s
B. 260 m/s
C. 328 m/s
D. 450 m/s

Answer

C

Explanation

`n_(1)/n_(2) = l_(2)/l_(1) = (102.5)/100 = 41/40`
as there are 4 beats and `n_(1) gt n_(2) :. n_(1) = n_(2) + 4`
` :. (n_(2) +4)/n_(2) = 41/40 :. 41 n_(2) = 40 n_(2) + 160`
` :. n_(2) = 160 " Hz and " n_(1) = 164` Hz
and ` v = 2n_(1) l_(1) = 2 xx 164 xx 1 = 328 ` m/s.