Question

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

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

Answer: (D)

Velocity of sound $=330 \, ms^{- 1}$
Length of closed pipe $=22 \, cm=22\times 10^{- 2}m$
The fundamental frequency of the stationary wave,
$\nu_{0}=\frac{v}{4 l}=\frac{330}{4 \times 22 \times 10^{- 2}}$
$=\frac{330 \times 10^{2}}{4 \times 22}=\frac{3000}{8}$
$\nu_{0}=375 \, Hz$
$3\nu_{0}=375\times 3=1125 \, Hz$
$5\nu_{0}=5\times 375=1875 \, Hz$
$5^{th}$ harmonic
Number of nodes $=3$
Note: In a closed pipe, odd harmonics are produced.