Page 135 - Physics - XI

Resonance Tube Apparatus

The apparatus consists of a cylindrical glass tube AB about 100 cm long with about 5 cm diameter. The
tube is fi xed with a vertical wooden stand along the side of a metre scale. The zero of the scale coincides
with the upper end of the glass tube. The lower end of the tube is attached to a reservoir R with the help of
a rubber tube. The reservoir can be moved up and down, so one can adjust the level of water in the glass
tube AB. A pinch cock P is provided with the rubber tube which is used for fi ne adjustments of the water
level in the tube AB (Fig. 10.1). The whole apparatus is fi xed on a horizontal wooden base. The wooden

base can be levelled using the screws provided at the bottom.

Principle/Theory
Let n be the frequency of the tuning fork and l be the length of the air column for the fi rst resonance
1
position as shown in Fig. 10.1, we have
λ
l + x = …(1)
1 4
where λ is the wavelength of the stationary wave produced and x is the end correction.

When the water level in the resonance tube AB is lowered so that the length of air column is little more
than three times the length of the fi rst air column (l ), then again loud sound is heard. This is known as the
1
length of the air column for the second resonance position l . In this case,
2
3λ
l + x = …(2)
2 4
From (1) and (2), we get

λ
l – l =
2 1 2
λ = 2(l – l ) …(3)
2 1
Let v be the velocity of sound at room temperature, then

v = nλ …(4)

On putting the value of λ from equation (3) to equation (4), we get
v = 2n(l – l ) …(5)
2
1
Equation (5) gives the velocity of sound at room temperature.
Procedure

1. Set the resonance tube apparatus vertical with the help of a plumb line and by adjusting the levelling
screw S-S provided at the bottom of the apparatus.
2. Fix the reservoir to the highest point of the rod.

3. Note the room temperature with the help of a thermometer and fi ll the reservoir with water such that
the level of water in the glass tube reaches up to its open end.
4. Lower down the reservoir, keeping the pinch cock tight.

5. Strike the tuning fork gently on the rubber pad and put it just above the open end A of the resonance
tube in such a way so that its prongs vibrate in a vertical plane. Slowly loosen the pinch cock and allow

133