Question

A open organ pipe containing air resonates in fundamental mode due to a tuning fork. The measured value of length `l` (in cm) of the pipe and radius `r` (in cm) of the pipe are `l=94.0+-0.1, r=5.0+-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 thus experiment, will be,
A. `0.16`
B. `0.64`
C. `1.2`
D. `1.6`

Answer 1

Correct Answer - A
`f=v/(2(l+2xx0.6r))=v/(2(l+1/2r)`
`:.(/_f)/f=(/_v)/v=(/_(l+1.2r))/((l+1.2r))`
Here `(/_v)/v=0`
`(/_f)/fxx100=-((/_l+1.2/_ ))/((l+1.2r))xx100`
`=0.16`