A resonance tube closed at one end is of height 1.5 m . A tuning fork of frequency 340 Hz is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is . (Neglect end correction, speed of sound in air =340 ~m / s )

Step-by-step solution

For a resonance tube, In the first mode, we have n = V 4 ~L _ j or L ₁= V 4 n = 340 4 340 =0.25 ~m =25 ~cm In this case L ₁= 4 =25 ~cm =100 ~cm Resonance can also be obtained when the length of the air column is 3 4 , 5 4 , 7 4 etc. At 5 4 = 5 100 4 =125 ~cm it stops as length of tube is 1.5 ~m =150 ~cm . Hence the minimum height of water =150-125=25 ~cm