Question

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

Answer 1

Correct Answer - A
`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%`