For a certain organ pipe, three successive resonant frequencies are observed at 300 Hz. 420 Hz and 540 Hz. The speed of sound in air is 340 `ms^(-1)`, The pipe is a

Options

A. closed pipe of length `11/12` m
B. open pipe of length `11/12` m
C. closed pipe of length `17/12` m
D. open pipe of lenth `17/12` m

Answer

c

Explanation

The successive resonant frequencies are 300 Hz,
420 Hz and 540 Hz.
`because 300 : 420 : 540 = 60 xx 5 : 60xx7: 60xx9 = 5 : 7 : 9`
As only harmonics are heard, the organ pipe is closed at
one end.
`therefore ` The fundamental frequency is 60 Hz.
`therefore n=v/(4L)`
`therefore 60=340/(4L)`
`therefore L=340/(4xx60)=340/240`
`=17/12`m