An organ pipe closed at one end has a harmonic with a frequency of 500 Hz. The next higher harmonic in an organ pipe closed at one end but of double length has frequency 350 Hz. Which of the following option is correct? (speed of sound in air is `340m//s`)

Options

A. Length of first organ pipe is 85 cm and it was vibrating in `5^(th)` harmonic
B. Length of first organ pipe is 170 cm and it was vibrating in `5^(th)` overtone
C. Length of first organ pipe is 85 cm and it was vibrating in `5^(th)` overtone
D. none of these

Answer

A

Explanation

First case `((2n-1)v)/(4l)=500`
second case `((2n+1))/(8l)=350`
dividing `(2(2n-1))/(2n+1)=(10)/(7)`
`10n+5=14n-7`
`n=3`
`5^(th)` harmonic `2^(nd)` overtone I first case
`=(5xx340)/(4xxl)=500`
`l=85cm`