A pipe `30.0cm` long is open at both end. Which harmonic mode of the ppipe resonates with a `1.1 k Hz` source ? If one end of the pipe is closed, what is the frequency of second overtone produced ? Take speed of sound in air as `330ms^(-1)`

Options

A. `second, 275Hz`
B. `second, 825Hz`
C. `third, 825Hz`
D. `second, 1375Hz`

Answer

D

Explanation

Here, `L=30.0cm=0.30m, upsilon=330ms^(-1)`
Let `nth` harmonic of open pipe resonate with `1.1kHz`
`i.e., v_(n)=1.1kHz=110Hz`
As`v_(n)=(n upsilon)/(2L)` or `n=(2Lv_(n))/(upsilon)=(2xx0..30xx1100)/(330)=2`
If one end of pipe is closed, then frequency of the second overtone is the frequency of fifth harmonic which is given by
`v^(')=(5upsilon)/(4L)=5xx(3300)/(4xx0.30)=1375Hz`