Question

L plunger

A plunger can be moved back and forth in a hollow tube that is L = 150 cm long with two open ends. A stretched wire is placed near the open end, as shown in the figure. The l = 50.0 cm long, 5.0 gram wire is fixed at both ends and oscillates in its fundamental mode. By resonance (meaning that the frequency of the string equals the frequency of the air column in the tube), the string sets the air column in the tube into oscillation at the column’s fundamental frequency when the plunger is first pulled a distance x = 20 cm from the top opening of the tube. (The air column in the tube thus amplifies the noise produced by the string oscillating in air just as the body of a guitar or violin amplifies the sound created by an oscillating string.) Find (a) this fundamental frequency and (b) the tension in the string. Note, the open side of the tube would be considered a “free” boundary whereas the plunger side would be considered a “fixed” boundary. (c) Also, determine all the additional locations x the plunger can be positioned along the length of the tube in order to achieve resonance between the air column in the tube and this fundamental frequency of the string. The speed of sound in air is 340 m/s at standard temperature and pressure.

Answer 1

I50 on- L tunda/henta Q fsequency of string → h are In nesonate Ca) : V - 340 ux 20x102 0 2x 50xio2

ing which Sesonate with shing is given as n - 1, 3,5, ?, -. 9( =20cm 2ccm 60 cm yo cm