Chapter 17, Problem 038 The water level in a vertical glass tube 1.00 m long can

Question

Chapter 17, Problem 038 The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 737 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.) Take the speed of sound to be 343 m/s. (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? What are the (b) least and (c) second least water heights in the tube for resonance to occur? (a) (b) Number (c) Number Units Units(

Explanation / Answer

Possible frequencies formed in closed pipe are

n = v/4l

n1 = 3n

n2 = 5n

n3 = 7n

......................

Fundamental Frequency is n = 737 Hz = v/4l

l = v/(4*n) = 343/(4*737) = 0.116 m

for next frequency

n1 = 3*(v/4l)

737 = 2*343/(4*l)

l = 0.232 m

For next frequency

n2 = 5*v/(4l)

737 = (5*343)/(4*l)

l = 0.582 m

For next frequency

n3 = 7*v/(4l)

737 = 7*343/(4*l)

l = 0.814 m

For next frequency

n4 = 9*v/(4*l)

737 = (9*343)/(4*l)

l = 1.04 m

so the no.of positions are 4

b) least water height is l1 = 1-0.814 = 0.186 m

c) second least water height is l2 = 1-0.582 = 0.418 m

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