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A pipe 30 cm long, is open at both ends. Which harmonic mode of the pipe resonates a 1.1 kHz source? (Speed of sound in air = 330 m `s^(-1)`)
A. First
B. Third
C. Second
D. Fourth

1 Answer

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Best answer
Correct Answer - B
Here,
Speed of sound,v=`330ms^(-1)`
Length of pipe,L=30cm=`30xx10^(-2)m`
In a open pipe (open at both ends), the frequency of its `n^(th)` harmonic is
`upsilon_(n)=(nv)/(2L)` where n=1,2,3,,……..
`thereforen=(2Lupsilon_(n))v`
Let `n^(th)` harmonic of open pipe resonate with 1.1 kHz source.
`thereforeupsilon_(n)=1.1kHz=1.1xx10^(3)Hz`
`thereforen=(2xx30xx10^(-2)xx1.1xx10^(3))/330=2`

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