The water level in a vertical glass tube 2.00 m long can be adjusted to any posi
ID: 1777076 • Letter: T
Question
The water level in a vertical glass tube 2.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 667 Hz is held just over the open top end of the tube, to set up a standing wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a tube with one end closed and the other end open.)
(a) For how many different positions of the water level will sound from the fork set up resonance in the tube's air-filled portion?
(b) What is the least water height in the tube for resonance to occur?
(c) What is the second least water heights in the tube for resonance to occur?
Explanation / Answer
(a) closed pipe: =4L , f=v/ , f=v/4L , L=nv/4f. where n = 1,3,5,7,....
when v=330m/s. Positions for odd harmonics are
1=0.124m (n =1), 2=0.371m (n=3), 3=0.618m, 4=0.866m (for n=7)
5=1.113m (for n =9), 6=1.360m (for n =11), 7=1.608m(for n =13), 8=1.855m (for n =15) ,
9 = 2.102 (for n = 17) It is out of size
when v=343m/s.
1=0.128m, 2=0.385m, 3=0.643m, 4=0.900m
5=1.157m, 6=1.414m, 7=1.671m, 8=1.928m, 9 = 2.185(Out of size)
(b)
when v=330m/s: 2 -1.855= 0.145= 14.5[cm]
when v=343m/s: 2 -1.928= 0.072= 7.2[cm]
(c)
when v=330m/s: 2 -0.124= 1.876[m]
when v=343m/s: 2 -0.128= 1.872[m]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.