A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____ cm . (Velocity of sound in air is 340 ms - 1 )

Step-by-step solution

We know that, v = λ f , then, λ = v f = 340   m   s - 1 340   Hz = 340   m   s - 1 340   s - 1 = 1   m First resonating length, l 1 = λ 4 = 100 4 = 25   cm Second resonating length, l 2 = 3 λ 4 = 3 × 100 4 = 75   cm Third resonating length, l 3 = 5 λ 4 = 5 × 100 4 = 125   cm So third resonance is not possible since the length of the tube is 125   cm Thus, minimum height of water necessary for resonance = 125 − 75 = 50 &#