A pipe of 30 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 1.1 kHz source ?
Given speed of sound in air `=330 ms^(-1)`.

Options

A. Third harmonic
B. Fifth harmonic
C. Second harmonic
D. Fourth harmonic

Answer

C

Explanation

Here,
Speed of sound, `v=330m s^(-1)`
Length of pipe, `L=30cm = 30 xx 10^(-2)m`
In an open pipe (open at both ends), the frequency of its `n^(th)` harmonic is
`upsilon_(n)=(nv)/(2L)` where `n= 1, 2, 3, .....`
`:.n=(2L upsilon_(n))/(v)`
Let `n^(th)` harmonic of open pipe resonate with 1.1 kHz source.
i.e., `upsilon_(n)=1.1kHz = 1.1xx10^(3)`Hz
`:.n=(2xx30xx10^(-2)xx1.1xx10^(3))/(330)=2`