Experimental Physics - 7

Principle:
If a vibrating tuning fork is held over the open end of the resonance tube T filled with water, as shown in fig12.9(a) then resonance is obtained at some position as the level of water is lowered. If E is the end correction of the tube and l₁ is the length from the water level to the top of the take, then




Where v is the velocity of sound in air and f is the frequency of tuning fork or air column.
Now, the water level is reduced to alower value, as shown in fig 12. 10(b). until a resonance is again obtained. If l₂ is new length of air column and ₂ is the wavelength of sound wave, then

Substracting equation (12.8) from (12.9), we get

Eliminating from equation (12.8) and (12.9), we get
     l₂ + e = 3(l₁ + e)
or e =

METHOD:
(i) The resonance tube is leveled Vertically with the help of a plumb line and the leveling screws. the reservoir and some part of the tube is filled with water.

(ii) The pinchcock is released and the level of water is adjusted close to the top end of the tube. then, the pinchcock is closed and the position of the reservoir is lowered.

(iii) The tuning fork is struck against a rubber pad and the vibrating tuning fork is placed just above the open end of the resonance tube so that the prongs of the fork vibrate in avertical plane. Now, the pinch-cock is slowely opened and the watr level in the tube is allowed to fall gradually. At the position when the air column is in resonance with turning fork, the position of the water level is noted.

(iv) Now, the pinch-cock is closed and level of reservoir is raised. The step (iii) is repeater by opening the pinch-cock. thus two readings of the first resonance position are recorded: one by lowering the water level in the tube and the other by raising the water level in the tube. The length of air column at this position is given by l₁

(v) Now, the level of the water in the tube is decreased such that air column in the tube becomes three times l₁. Once again, two readings of water are taken in accordance with step (iii) and (iv) at which it comes in resonance with the tuning fork. This reading is recorded as second resonance condition of the tube with tuning fork. This Reading is recorded as second resonance condition of the tube with turning fork. This reading is recorded assecond resonance condition of the tube with tuning fork. This Reading is recorded as second resonance condition of the tube with tuning fork. The length of the air column at this condition is given by l₂.

Illustration: The velocity of sound in air is measured using a resonance tube method. The observation madedring the Experiment are as follows:
Frequancy of first tuning fork f₁ = 480 Hz.
Frequancy of second tuning fork f₁ = 512 Hz.
Position of upper end of the Tube, L₁ = 0.2 cm.
Room temperature T = 25⁰c

Frequency of fork	Resonance	Position of water level of resource l2 (cm) Water falling       Water rising     mean l2	Mean length of air column L2 - L1 (cm)
480	First Second	17.0                           17.2 52.4                           52.6
512	First Second	16.4                           16.2 49.9                           50.1

Calculate:
(i) The velocity of sound at room temperature.
(ii) The End correction for the tube.
Solution:- The observation table is completed as shown below:

Frequency of fork (Hz)	Resonance	Position of water level of resource l2 (cm) Water falling       Water rising     mean l2	Mean length of air column L2 - L1 (cm)
480	First Second	17.0                           17.2            17.1 52.4                           52.6            52.5	l1 = 16.9 l2 = 52.3
512	First Second	16.4                           16.2            16.3 49.9                           50.1            50.0	l1 = 16.1 l2 = 49.8

(i) Velocity of sound:
f₁ = 480Hz ; l₁ = 16.9 m ; l₂ = 52.3 cm = 0.523 m

V₁ = 2f₁(l₂ - l₁)

          = 2(480)(0.523 - 0.169) = 340 m/s
For f₂ = 512 Hz ; l₁ = 16.1cm = 0.161 = 0.161m ; l₂ = 49.8 = 0.498m
V₂ = 2f₂(l₂ - l₁)

or V₂ = 2(512)(0.498 - 0.161) = 345 m/s
The average velocity of sound is

(ii) End - correction of the tube
For f₁ = 480 Hz


For F₂ = 512 Hz


The average end correction is