5) Dr. Scott has a tube that can be either open or closed at either end. He exci

Question

5) Dr. Scott has a tube that can be either open or closed at either end. He excites a vibration in the air in the tube, and you hear two loud frequencies, 210 Hz and 240 Hz, and you are told that they are consecutive frequencies. Assume the speed of sound is 340 m/sec. The length of the tube 5 and 2/3 meters (5.6666 m, etc.) a) Calculate the lower frequencies in this sequence and find the fundamental (lowest) frequency b) Is this a tube that is open at both ends or open at one end and closed at the other?

Explanation / Answer

Given,

v = 340 m/s ; L = 5.666 m

f = 210 Hz and f' = 240 Hz

We know that for a tube with one end open/closed

f1 = v/2L

f1 = 340/2 x 5.6666 = 30 Hz

The given freqncies are, f = 210 and 240 Hz

Clearly they are the 7th and 8th frequencies. So the lowest frequencies are

f1 = 30 Hz

f2 = 2 x 30 = 60 Hz

f3 = 3 x 30 = 90 Hz

f4 = 4 x 30 = 120 Hz

f5 = 5 x 30 = 150 Hz

f6 = 6 x 30 = 180 Hz

b)The given tube is opened at both the ends.

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