Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called it fundamental frequency, whose wavelength is denoted as lambda_(t). Match each system with statements given in Column II describing the nature and wavelength of the standing waves.

Column I shows four systems, each of the same length L, for producing

1.	Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called it fundamental frequency, whose wavelength is denoted as lambda_(t). Match each system with statements given in Column II describing the nature and wavelength of the standing waves.
Answer» Solution :In case of pipe we can PRODUCE LONGITUDINAL waves and for strings we produce transverse waves. `A rarr (p, t)` : It is a closed organ pipe hence in case of fundamental vibrations length of the tube must be `((1)/(4))^(th)` of the wavelength (half loop). `(lambda_(t))/(4)= L rArr lambda_(t) = 4L` `B rarr (p, s)` : It is open organ pipe hence in case of fundamental vibrations length ofthe pipe must be half of the wavelength (one loop). `(lambda_(t))/(2) = L rArr lambda_(t) = 2L` `C rarr (q, s)` : It is a case of string of length L fixed at both ENDS. In case of fundamental vibrations length of the pipe must be half of the wavelength (one loop). `(lambda_(t))/(2) = L rArr lambda_(t) = 2L` `D rarr (q, r)` : In this case mid-point is fixed hence half-length must form one loop. `(lambda_(t))/(2) = (L)/(2) rArr lambda_(t) = L`