An organ pipe P1, closed at one end vibrating in its first harmonic and another pipe P2, open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of p1 to that of P2, is

Let l1 and l2 be the respective lengths of the closed and open organ pipes. The frequency of vibration of a closed pipe in r th mode of vibration is given bynr=(2r−1)V4l1 For first harmonic, r= 1 n1=V4l1  For open pipe, nr=rV2l2  For third harmonic, =3V2l2 V4l1=3V2l2  or  l1l2=13