Answer to Question #283279 in Physics for riki

Question

A tube 1.20 m long is closed at one end. A stretched wire

is placed near the open end. The wire is 0.330 m long and has a

mass of 9.60 g. It is fixed at both ends and oscillates in its funda-

mental mode. By resonance, it sets the air column in the tube into

oscillation at that column’s fundamental frequency. Find (a) that

frequency and (b) the tension in the wire.

Answer 1

Find the frequency (the speed of sound is 343 m/s):

$$f=\dfrac{c}{4·L_p}=\dfrac{343}{4·1.2}=71.5\text{ Hz}.$$

Find the tension:

$$T=4mL_wf^2=64.8\text{ N}.$$