An open organ pipe containing air resonates in fundamental mode due to a tuning fork. The measured values of length `l` (in cm) of the pipe and radius r (in cm) of the pipe are `l=94+-0.1`,`r=5+-0.05`. The velocity of the sound in air is accurately known. The maximum percentage error in the measurement of the frequency of that tuning fork by this experiment will be

Options

A. `0.16`
B. `0.64`
C. `1.2`
D. `1.6`

Answer

A

Explanation

`f=(v)/(2(l+2e))` where `e=`end correction `=0.6r`
`:. f=(v)/(2(l+2xx0.6r))=(v)/(2(l+1.2r))`
`:. (Delta f)/(f)=(Delta v)/(v)-(Delta (l+1.2r))/(l+1.2r)=(Deltav)/(v)-(Delta l+1.2Delta)/(l+1.2r)`
Here, `(Deltav)/(v)=0` (given)
`(Deltaf)/(f)xx100=-(Delta l+1.2Delta r)/(l+1.2r)xx100`
For maximum `%` error `Delta lamda=0.1Delta r=0.05`
`((Delta f)/(f)xx100)_(max)=(0.1+1.2xx0.05)/(94+1.2xx5)xx100`
`=0.16%`