A pipe `30.0` cm long is opened at both ends. Which Harmonic mode of the pipe will be at `1.1` kHz frequency also find fundamental frequency, if one end of the pipe is colsed. Take the speed of sound in air as 330 `"ms"^(-1)`

Options

A. 2nd harmonic and 275 Hz
B. 1st harmonic and 260 Hz
C. 3rd harmonic and 260 Hz
D. Fundamental harmonic and 240 Hz

Answer

a

Explanation

Here, `L = 30.0` cm `=0.3` cm
Let, nth harmonic of open pipe is at a frequency of 1 kHz,
i.e. `v_(n) = 1.1" kHz"= 1100` Hz
As, `v_(n) = (nv)/(2L)`
`therefore n =(2Lv_(n))/v=(2xx0.30xx1100)/330=2`
i.e. 2nd harmonic of the open pipe will present.
If one end of pipe is closed, its fundamental frequency
`n=0" in " v_(0)=(2n+1)v/(4L)`
` v_(1)=v/(4L)=330/(4xx0.3)=275` Hz