The water level in a vertical glass tube 1.20 m long can be adjusted to any posi

Question

The water level in a vertical glass tube 1.20 m long can be adjusted to any position in the tube. A tuning fork vibrating at 805 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.)

(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?

(b) What is the least water height in the tube for resonance to occur?

(c) What is the second least water heights in the tube for resonance to occur?

Explanation / Answer

In open tube

let length of the air column = l = L-h

h = water level

under resonsnce

l = n*lambda/4

n = 1 , 3, 5 , ......

frquency f = v/lambda = nv/4l = nv/(4*(L-h))

given f = 805

for h = 0

805 = n*343/(4*(1.2))

n = 11

(a)

for 11 different positions

(b)

for n = 11

805 = 11*343/(4*(1.2-h))

h = 0.028 m = 2.8 cm

(c)

for n = 10

805 = 10*343/(4*(1.2-h))

h = 0.135 m = 13.5 cm

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