Question

A closed pipe of length $22cm$ , when excited by a $1875Hz$ source forms standing waves. The number of pressure nodes formed in the pipe are [velocity of sound in air $=330m{s}^{-1}$ ]

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

Answer: (D)

Velocity of sound $=330m{s}^{-1}$
Length of closed pipe $=22cm=22\times 10^{-2}m$
The fundamental frequency of the stationary wave,
${\nu }_0=\frac{v}{4l}=\frac{330}{4\times 22\times 10^{-2}}$
$=\frac{330\times 10^2}{4\times 22}=\frac{3000}{8}$
${\nu }_0=375Hz$
$3{\nu }_0=375\times 3=1125Hz$
$5{\nu }_0=5\times 375=1875Hz$
$5^{th}$ harmonic
Number of nodes $=3$
Note: In a closed pipe, odd harmonics are produced.