Two closed organ pipes of length 100 cm and 101 cm produce 16 beats in 20 sec. When each pipe is sounded in its fundamental mode calculate the velocity of sound in m/s.

Options

A. 303
B. 332
C. `323.2`
D. 330

Answer

C

Explanation

For first cloed pipe,
`f _(1) = (v)/(4L) = (v)/( 4 xx 100) = (v)/(400)`
For second closed, pipe,
`f._(1) = (v)/(4L), = (v)/(4 xx 101) =(v)/(404)`
`implies f _(1) gt f _(1)`
Here, `f _(1) -f ._(1)= (16)/(20)= ("totla no. of beats")/(total time")`
`therefore (v)/(400)-(v)/(404) = (16)/(20)`
`therefore v ((404 - 400)/(400 xx 404))= (16)/(20)`
`therefore v = 32320 cm //s =323.2 m//s`