JEE Main & Advanced Physics Wave Mechanics Quink's Tube

This is an apparatus used to demonstrate the phenomenon of interference and also used to measure velocity of sound in air. This is made up of two U-tube A and B as shown in figure. Here the tube B can slide in and out from the tube A. There are two openings P and Q in the tube A. At opening P, a tuning fork or a sound source of known frequency n0 is placed and at the other opening a detector is placed to detect the resultant sound of interference occurred due to superposition of two sound waves coming from the tubes A and B.

Initially tube B is adjusted so that detector detects a maximum. At this instant if length of paths covered by the two waves from P and Q from the side of A and side of B are \[{{l}_{1}}\] and \[{{l}_{2}}\] respectively then for constructive interference we must have

\[{{l}_{2}}-{{l}_{1}}=N\lambda \]                                               .... (i)

If now tube B is further pulled out by a distance \[x\] so that next maximum is obtained and the length of path from the side of B is \[{{l}_{2}}'\] then we have

\[l{{'}_{2}}={{l}_{2}}+2x\]                                              .... (ii)

where \[x\] is the displacement of the tube. For next constructive interference of sound at point Q, we have \[l{{'}_{2}}={{l}_{1}}=(N+1)\lambda \]                                     .... (iii)

From equation (i), (ii) and (iii), we get

\[l{{'}_{2}}-{{l}_{2}}=2\times x=\lambda \]\[\Rightarrow \]\[x=\frac{\lambda }{2}\]

Thus by experiment we get the wavelength of sound as for two successive points of constructive interference, the path difference must be \[\lambda \]. As the tube B is pulled out by \[x,\] this introduces a path difference \[2x\] in the path of sound wave through tube B. If the frequency of the source is known, \[{{n}_{0}},\] the velocity of sound in the air filled in tube can be gives as \[\nu ={{n}_{0}}.\lambda \]\[=2{{n}_{0}}x\]