A pipe 17 cm long is closed at one end. Which harmonic mode of the pipe resonates a 1.5 kHz source? (Speed of sound in air = 340 m `s^(-1)`)

Options

A. First
B. Third
C. Fifth
D. Seventh

Answer

B

Explanation

Here speed of sound,v=`340ms^(-1)`
Length of pipe,L=17 cm=`17xx10^(-2)m`
In a closed pipe (open at one end), the frequency of its `n^(th)` harmonic is
`upsilon_(n)=(nw)/(4L)`where n=1,3,5,7….
Let `n^(th)` harmonic of closed pipe resonates with 1.5 kHz source.
`thereforeupsilon_(n)=1.5xx10^(3)Hz`
`therefore1.5xx10^(3)=(nw)/(4L)`
`n=(1.5xx10^(3)xx4xx17xx10^(-2))/340,n=3`