In resonance tube experiment , the velocity of sound is given by `v = 2 f_(0) ( l_(2) - l_(1))` . We found `l_(1)=25.0 cm` and `l_(2)=75.0 cm`. If there is no error in frequency, what will be the maximum permissible errror in the speed of sound ? (Take `f_(0) = 325 Hz`)

Options

A. `0.2m//s`
B. `0.65m//s`
C. `1.3m//s`
D. `2.6m//s`

Answer

C

Explanation

`V=2f_(0)(l_(2)-l_(1))`, `(dv)=2f_(0)(dl_(2)-dl_(1))`
`(dv)_(max)=max of [2f_(0)(+-Deltal_(2)overset(-)(+)Deltal_(2))]`
`=2f_(0)(Deltal_(2)+Deltal_(1))`
`l_(1)=25.0cm`
`impliesDeltal_(1)=0.1cm` (place value of last number)
`l_(1)=75.0cm`
`implies Deltal_(2)=0.1cm`(place value of last number)
So max permissible error `i` speed of sound
`(dv)_(max)=2(325Hz)(0.1cm+0.1cm)`
`=1.3m//s`
`V=2f_(0)(l_(2)-l_(1))`
`=2(325Hz)(75.0cm-25.0cm)=325m//s`
so `V=(325+-1.3)m//s`