A vertical glass pipe closed at the bottom end ispartially filled with water. A

Question

A vertical glass pipe closed at the bottom end ispartially filled with water. A tuning fork vibrating at an unknownfrequency is placed near the top of the pipe. The lengthL of the air column above the water level (see figure below) canbe adjusted by removing or adding water via a tube connected to thebottom end of the pipe. The water’s surface acts like a wallat the top end and thus make it a one-end-closed tube. The soundwaves generated by the fork are reinforced whenL corresponds to one of the resonance

frequencies of the pipe. For a certain tube, thesmallest value of L for which a peak occurs in the sound intensity is 9.00 cm. (a)What is the frequency of the tuning fork? (Take speed of sound inair to be 343 m/s)

(b) What is the value of L for the next two resonance frequencies?

Answers: (a) 953 Hz (b) 27 cm, 45 cm

Explanation / Answer

L0 = 9.00 cm, v = 343 m/s a) /4 = L0, so = 4L0 = 36.0cm f = v/ = 953 Hz b) L = (2k + 1)/4 = (2k + 1)*L0 next two L are: L = 3L0 = 27.0 cm and 5L0 =45.0 cm

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