In fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is t second. The frequency of vibration of air column is ( = wavelength of the wave)

Step-by-step solution

Let the length of the closed pipe be L . The time taken by the sound wave to travel the length of the pipe is t . The speed of the sound wave is v = L t . In the fundamental mode of a closed pipe, the length of the air column is related to the wavelength by L = 4 . The frequency of vibration is given by f = v . Substituting v = L t and = 4L , we get: f = L/t 4L = 1 4t = 0.25 t Answer: 0.25 t