An air column in a glass tube , is open at one end and closed at the other by a movable piston . The air in the tube is warmed above room temperature , and a 384 Hz tuning fork is held at the open end. Resonance is heard when the piston is 22.8 cm from the open end and again when it is 68.3 cm from the open end . (a) What speed of sodium is impliedby these data ? (b) How far from the open end will the piston be when the next resonance is heard ?

An air column in a glass tube , is open at one end and closed at the o

1.	An air column in a glass tube , is open at one end and closed at the other by a movable piston . The air in the tube is warmed above room temperature , and a 384 Hz tuning fork is held at the open end. Resonance is heard when the piston is 22.8 cm from the open end and again when it is 68.3 cm from the open end . (a) What speed of sodium is impliedby these data ? (b) How far from the open end will the piston be when the next resonance is heard ?
Answer» SOLUTION :The resonance is heard as amplification , when all the air in the tube vibrates in a standing - wave pattern along with the TUNING fork . The air vibration has a node at the piston and an antinide at the top end . For an air column closed at one end , resonances will occur when the length of the column is equal to `lambda//4 , 3 lambda//4 , 5 lambda//4` and so on . Thus , the CHANGE in the length of the pipe from one resonance to the nextis `d _(NN) = lambda//2`. In this case, `lambda//2 = ( 0.683 - 0.228 )m = 0.455 m` and ` lambda = 0.910 m` a. ` v = f lambda = ( 384 Hz) ( 0.910 m) = 349 m//s` `b. L = 0.683 m + 0.455 m = 1.14 m`