A Pipe open at one end has length 0.8 m. At the open end of the tube a string 0.5 m long is vibrating in its first overtone and resonates with fundamental frequency of pipe. If tension in the string is 50 N, the mass of string is (Neglect end correction) (Speed of sound = 320 m/s)

Step-by-step solution

The fundamental frequency of a pipe open at one end (closed pipe) is given by f_p = v 4L_p . Substituting the given values, f_p = 320 4 0.8 = 100 Hz. The string is vibrating in its first overtone, which corresponds to the second harmonic. The frequency of the string is f_s = 2 2L_s T = 1 L_s T . Since the string resonates with the pipe, f_s = f_p . 1 0.5 50 = 100 2 50 = 100 50 = 50 Squaring both sides, we get 50 = 2500 = 50 2500 = 0.02 kg/m. The mass of the string is m = L_s = 0.02 0.5 = 0.01 kg. Converting to gram