Question

A long glass tube is held vertically, dipping into water, while a tuning fork of frequency 512 Hz is repeatedly struck and held over the open send. Strong resonance is obtained, when the length of the tube above the surface of water is 50 cm and again 84 cm, but not at any intermediate point. Find the speed of sound in air and next length of the air column for resonance.

Answer 1

Glass tube dipped in water will act as a resonance tube , and velocity of sound in a resonance tube is given by ,

$v=2f(l_2-l_1)$ ,

given $l_1=50cm=0.50m,l_2=84cm=0.84m,f=512Hz$ ,

therefore $v=2\times 512(0.84-0.50)=348.16m/s$ ,

let the next length is $l_3$ for resonance ,

hence , $v=2f(l_3-l_2)$ ,

or $(l_3-l_2)=v/2f$ ,

or $(l_3-0.84)=340/(2\times 512)=0.34$ ,

or $l_3=0.34+0.84=1.18m=118cm$