A pipe open at both ends of length 1.5 m is dipped in water at one end such that 2^ nd overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of sound in air =330 ~m / s ) (Neglect end correction)

Step-by-step solution

A pipe open at both ends and partly immersed in water functions as a closed organ pipe. The resonant frequencies of a closed pipe are f_n = (2n-1)v 4l , where n is the harmonic number, v is the speed of sound, and l is the length of the air column. The second overtone corresponds to the third harmonic ( n=3 ). Given f = 330 , Hz and v = 330 , m/s , for resonance with the second overtone: 330 = 5 330 4l Simplifying, 1 = 5 4l , so l = 5 4 = 1.25 , m . The total pipe length is 1.5 , m , so the immersed length is 1.5 -