In resonance apparatus for determining the velocity of sound in air, a turnning fork of frequency 320 Hz is used. A loud sound is heard when water level is at 24.8 cm and then at 78.5 cm. These lengths are called the first and second resonance lengths of air column in the resonance apparatus. Calculate the velocity of sound in air within the limits of permissiblr error.

Explanation

The velocity of sound in air using two resonance method is given by
`v=2n (l_(2)-l_(1))` …(i)
where n is frequency of the tunning fork, and `l_(1)` and `l_(2)` are the first and second resonance lengths.
`:. V=2xx320xx(78.5-24.8)`
`=640xx53.7=34368 cm//s=343.68 m//s`
The relative error in velocity of sound is given by
`(Deltav)/v=(Delta(l_(2)-l_(1)))/((l_(2)-l_(1)))=(Deltal_(2))/((l_(2)-l_(1)))+(Delta l_(1))/((l_(2)-l_(1)))`
`=0.1/53.7+0.1/53.5=0.2/53.7=0.0037`
`:. Deltav=0.0037xx343.68=1.27 m//s`
Thus, velocity of sound is `(343.68 pm 1.27) m//s`.