A closed organ pipe has length `L`. The air in it is vibrating in third overtone with maximum amplitude a . The amplitude at distance`(L)/(7)` from closed of the pipe is a) 0 b) a c) a/2 d) data insufficient

Answer

a

Explanation

Equation of stationary waves from closed end `= a sink x cos omegat`
Now at `x = (l)/(7)`
`(7lambda)/(k) = l`
Amplitude `= a sin kx = a sin "(2pi)/(lambda) (l)/(7)`
`= a sin '(2pi)/(lambda) (7lambda)/(4 xx 7) = a sin '(pi)/(2) = a`