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3.33Solution :

In case of vibration in air column ,the antinpdes at the open ends (s) are located at a small distance outside the open end.This small distance is known as end correction.<br> The value of end correction e=0.3d, where d is the diameter of the tube. In case of a tube open at both ends,the effective length of the air column.<br>` implies 1'=1+2e` Where e=0.3d <br> Fundamental frequency in case `f_0=v/(21)` <br> `implies 320=(320)/(2(1+2e))` <br> `1+2e=1/2` <br> `0.48+2(0.3d)=1/2 implies d=1//30m=3.33cm` <br> Now one end is closed,the effective length of the tube <br> `1'=1+e`<br> `f_0=v/(4 1')=(v)/(4(1+e)) implies f_0=(320xx100)/(4(48+0.3xx3.33))=163.27 Hz` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/VMC_PHY_XI_WOR_BOK_03_C12_E05_062_S01.png" width="80%">