A resonance tube is old and has jagged end. It is still used in the laboratory to determine. Velocity of sound in air. A tuning fork of frequency `512Hz` produces first resonance when the tube is filled with wtaer to a mark 11 cm below a reference mark, near the open end of the tube. the experiment is repeated with another fork of frequency `256Hz` which produces first resonance when water reaches a mark `27 cm` below the reference mark. the velocity of sound in air, obtained in the experiment, is close to :

Options

A. `335 ms^(-1)`
B. `341 ms^(-1)`
C. `328 ms^(-1)`
D. `322 ms^(-1)`

Answer

C

Explanation

`f = (V)/(4L + 4e)`
`512 = (V)/(4 xx (11)/(100) + 4e)` …(i)
`256 = (V)/(4 xx (27)/(100) + 4e)` …(iii)
From equation (i) and (iii)
`2 = (4 xx (27)/(100) + 4e)/(4 xx (11)/(100) + 4e)`
`2 (0.11 + e) = 0.27 + e, 0.11 xx 2 + 2 = 0.27 + e, 2e - e = 0.27 -0.22`
Put in equation (i) `512 = (V)/(4 xx 0.11 + 4 xx 0.05)`
`V = 327.68 xx 512, V = 327.68 m//s`