A tube with a cap on one end, but open at the other end, has a fundamental frequ

ID: 1322650 • Letter: A

Question

A tube with a cap on one end, but open at the other end, has a fundamental frequency of 130.8 Hz. The speed of sound is 343.0 m/s.

(a) If the cap is removed, what is the new fundamental frequency of the tube?

(b) How long is the tube?

(i) The end cap must have been removed.

(ii) The end cap must be in place.

(iii) The given information does not make it possible to determine whether the end cap is in place or if it has been removed.

(d) The tube is observed to resonate at a frequency of 523.2 Hz. Which of the following statements is true?

(i) The end cap must have been removed.

(ii) The end cap must be in place.

(iii) The given information does not make it possible to determine whether the end cap is in place or if it has been removed.

fo = V/4L

L= V/4f = 343/(4*130.8) = 0.65

f = n*fo

n = 5

wave length = v/f = 0.52

with a cap on one end, but open at the other end

5*wavelength/4 = L

(5*0.52)/4 = 0.65

0.65 = 0.65

(ii) The end cap must be in place.

++++++++++++++++++++++++++++++++

with a cap removed fo = V/2L

L = 1.31 m

wavelength = v/f = 523.2/343 = 1.52

n = f/fo = 523.2/130.8 = 4

with a cap removed

(4*wavelength)/2 = L

(4*1.52)/2 = 3.04 is not equal to 1.32m

(iii) The given information does not make it possible to determine whether the end cap is in place or if it has been removed

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