A closed organ pipe has length ' λ '. The air in it is vibrating in 3 text rd overtone with maximum amplitude ' a '. The amplitude at a distance of λ / 7 from closed end of the pipe.

Question

A closed organ pipe has length ' λ '. The air in it is vibrating in 3 text rd overtone with maximum amplitude ' a '. The amplitude at a distance of λ / 7 from closed end of the pipe. (A) a (B) a/2 (C) (√3/2) a (D) (1/√2) a

Tardigrade Admin · Accepted Answer

The figure shows variation of displacement of particles in a closed organ pipe for

3^{rd}

overtone.
For third overtone

l = \frac{7 λ}{4}

or

λ = \frac{4 l}{7}

or

\frac{λ}{4} = \frac{l}{7}

Hence the amplitude at

P

at a distance

\frac{l}{7}

from closed end is '

a^{'}

because there is an antinode at that point.

Q. A closed organ pipe has length ' $λ$ '. The air in it is vibrating in $3^{rd}$ overtone with maximum amplitude ' $a$ '. The amplitude at a distance of $λ /7$ from closed end of the pipe.

a

a/2

$\frac{3}{2} a$

$\frac{1}{2} a$

Q. A closed organ pipe has length ' λ '. The air in it is vibrating in 3rd overtone with maximum amplitude ' a '. The amplitude at a distance of λ/7 from closed end of the pipe.

a

a/2

23​​a

2​1​a

The figure shows variation of displacement of particles in a closed organ pipe for 3rd overtone. For third overtone l=47λ​ or λ=74l​ or 4λ​=7l​ Hence the amplitude at P at a distance 7l​ from closed end is 'a′ because there is an antinode at that point.

Q. A closed organ pipe has length ' $λ$ '. The air in it is vibrating in $3^{rd}$ overtone with maximum amplitude ' $a$ '. The amplitude at a distance of $λ /7$ from closed end of the pipe.

$\frac{3}{2} a$

$\frac{1}{2} a$