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The water level in a vertical glass tube 1.00 m long can be adjusted to any posi

ID: 1657638 • Letter: T

Question

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 666 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?

Explanation / Answer

frequency is given as

f = (2n + 1) v/(2L)

where v = speed of sound = 343 m/s

f = 666 Hz

L = 1

666 = (2n + 1) (343)/(2 x 1)

n = 1

b)

at n =1

f = (2n + 1) v/(2L1)

666 = (2 (1) + 1) (343)/(2 L1)

L1 = 0.77 m

b)

at n =2

f = (2n + 1) v/(2L2)

666 = (2 (2) + 1) (343)/(2 L2)

L2 = 0.77 m