Resonance Column Experiment (Class 11) Readings
Resonance Column Experiment (Class 11) Readings
Experiment – 1
Aim
i. To find the velocity of sound in air at room temperature and hence at 0°C using a resonance column apparatus.
ii. To find the unknown frequency of the given tuning fork.
Apparatus
Resonance column apparatus, Tuning forks, Rubber hammer, Meter Scale etc.
Principle:
i. The velocity of sound at room temperature, V_{t} = 2n(l_{2}l_{1})
where, n = Frequency of the tuning fork
l_{1} = First resonating length
l_{2} = Second resonating length
ii. The velocity of sound at 0°C is given by V_{0} = V_{t}√(273/(273+t))
or V_{0} = V_{t} – 0.6t
where, t = Room temperature°C
iii. Unknown frequency, n’ = V_{t}/(2(l_{2}’l_{1}’))
Procedure
Length of the air column is kept very small. A tuning fork of known frequency (n) is excited and held horizontally over the mouth of the inner tube. The length of air column in the inner tube is slowly increased by raising the tube till a booming sound is heard. The length of the air column is measured (l_{1}). Keeping the tuning fork excited at the mouth of the tube the length of the air column is measured (l_{1}). Keeping the tuning fork excited at the mouth of the tube the length of the air column is increased further. The length (l_{2}) of the air column is measured when the booming sound is heard (l_{2}>3l_{1}). The experiment is repeated and the mean values of l1 and l2 are found out. The velocity of sound at room temperature is calculated. The experiment is repeated for different tuning forks and the mean value of V_{t} is found. From this the velocity of sound at 0°C is calculated.
Using the tuning forks of known frequencies the mean value of V_{t} is calculated. Then using the tuning fork of unknown frequency, the first and second resonating lengths (l_{1}’ and l_{2}’) are measured. The unknown frequency (n’) can be calculated.
Observations and Readings
Frequency of tuning fork (n) 
First resonance length (l_{1}) 
Second resonance length (l_{2}) 
V_{t} 

1(cm) 
2(cm) 
Mean (l_{1}’) 
1(cm) 
2(cm) 
Mean (l_{2}’) 

512 
16.5 
16.5 
16.5 
50.5 
50.5 
50.5 
34816 
480 
17.5 
17.5 
17.5 
53.5 
53.5 
53.5 
34560 
Unknown 
22.5 
22.5 
22.5 
68.5 
68.5 
68.5 

Mean V_{t }= 34688 cm/s = 346.88 m/s
Room temperature, t = 30°C
Velocity of sound at 0°C, V_{o} = V_{t} – 0.6t = 346.88 – 0.6 x 30 = 328.88 m/s
Unknown Frequency, n’ = V_{t}/(2(l_{2}’l_{1}’)) = 403.3 Hz
Results:
1. Velocity of sound at room temperature = 346.88 m/s
2. Velocity of sound at 0°C = 328.88 m/s
3. Unknown frequency = 403.3 Hz
Experiment  2
Aim: To compare the frequencies of two tuning forks and also to determine the end correction.
Principle:
Let l_{1} and l_{2} are the first and second resonance length with a tuning fork of frequency n_{1}, l_{1}’ and l_{2}’ respectively are the first and second resonance length with another tuning fork of frequency n_{2}. Then,
i. Ratio of frequencies, n_{1}/n_{2} = (l_{2}’l_{1}’)/(l_{2}l_{1})
ii. The end correction is given by, e = (l_{2}3l_{1})/2
Procedure:
The length of the air column is kept very small. The first tuning fork of frequency n_{1} is excited and is held horizontally close to the mouth of the inner tube. The inner tube is slowly raised until maximum sound is heard. The length of air column is measured as l_{1}. Then the inner tube is further raised, keeping the vibrating fork at the mouth of the tube, till the maximum sound is heard. The length of air column noted as l_{2}. Repeating this procedure for another tuning fork of frequency n_{2} and the resonance lengths are measured as l_{1}’ and l_{2}’. From this n_{1}:n_{2} is found out. The end correction is also calculated.
Observations and Readings
1. To compare the frequencies
Frequency of tuning fork (n) 
First resonance length 
Second resonance length 
(l_{2}’l_{1}’) / (l_{2}l_{1}) 

1(cm) 
2(cm) 
Mean 
1(cm) 
2(cm) 
Mean 

n_{1} = 512 
16.5 
16.5 
l_{1} = 16.5 
50.5 
50.5 
l_{2} = 50.5 
1.06 
n_{2} = 480 
17.5 
17.5 
l_{1}’ = 17.5 
53.5 
53.5 
l_{2}’ = 53.5 
Ratio of frequencies, n_{1}/n_{2} = 1.06
(l_{2}’l_{1}’)/(l_{2}l_{1}) = 1.06
2. To find the end correction
Tuning fork 
First resonance length (l_{1}) 
Second resonance length (l_{2}) 
e 

1(cm) 
2(cm) 
Mean 
1(cm) 
2(cm) 
Mean 

First 
16.5 
16.5 
16.5 
50.5 
50.5 
50.5 
0.50 
Second 
17.5 
17.5 
17.5 
53.5 
53.5 
53.5 
0.50 
Mean e = 0.5 cm = 0.5 x 10^{2} m
Results:
i. Frequencies of two tuning forks are compared.
ii. End correction = 0.5 x 10^{2} m
Simple Pendulum Experiment (Class 11) Readings
Simple Pendulum Experiment (Class 11) with Calculations and Readings
Aim
i. To verify the relation between period (T) and length (l) of pendulum
ii. To find out the acceleration due to gravity
iii. To determine the length of seconds pendulum
iv. To find the period of the pendulum whose length is 105 cm.
Apparatus
Simple pendulum, Stopwatch, Meter scale, Wooden block etc..
Principle
For small amplitudes of oscillation of a simple pendulum,
l/T^{2} = a constant where, l —> Length of the pendulum
T—> Period of the pendulum
Also, T = 2π√(l/g) where, g —> Acceleration due to gravity at the place
Therefore, g = 4π^{2}(1/T^{2})
Procedure
i. Relation between I and T^{2}
The bob is placed between two wooden blocks and its diameter (d) is measured. Hence radius (r = d/2) can be calculated. The length of the string (I) is so adjusted that the distance between the point of suspension and the bottom of the bob is (50 + r) cm. Hence the length of the pendulum ‘l’ is 50 cm.
A mark is made on the edge of the table using a piece of chalk to indicate the equilibrium position of the pendulum, ie. , the position of the pendulum when it is at rest. The bob is pulled aside through a small distance and released. The pendulum executes oscillations, after a few oscillations, a stop watch is started just when the pendulum crosses the equilibrium position. When it next crosses the mark in the same direction, the oscillations are counted and when the pendulum passes the chalk mark in the same direction for the 20th time, the stop watch is stopped.
Thus the time taken for 20 oscillations is determined. This is repeated and the mean time taken for 20 oscillations is found. Hence the time for one oscillation ie., period 'T' is calculated. l/T^{2} is also calculated.
The experiment is repeated for lengths 60, 70, 80, 90, 100,110 cm. In each case l/T^{2} is calculated. It is found to be a constant. This is the relation between the period and length of a simple pendulum. Graph is drawn with 'l' along the Xaxis and 'T^{2}' along the Yaxis. A straight line graph is obtained.
ii. Acceleration due to gravity at the place
The mean value of l/T^{2} is determined. Hence 'g' can be calculated using the formula g = 4π^{2}(1/T^{2}). Note AB and BC from the graph. Hence g can be calculated using the equation, g = 4π^{2}.AB/BC
iii. Length of the seconds pendulum
For a seconds pendulum, T = 2 seconds. Then T^{2}= 4. From the graph, the value of 'l’ for which T^{2} = 4 is found (OD). This gives the length of the seconds pendulum.
iv. Period of the pendulum whose length is 105 cm
From the graph the square of the period corresponding to the length 105 cm is noted (OE). The square root of this ( √OE ) gives the period.
Observations and Readings
Radius of the bob, r = 0.95 cm
No: 
Distance between point of suspension and the bottom of the bob (l+r) 
Length of the pendulum (l) 
Time for 20 oscillations (t) 
Period of oscillation (T=t/20) 
T^{2} 
l/T^{2} 

1 
2 
mean 


cm 
cm 
s 
s 
s 
s 
s^{2} 
cm/s^{2} 
1 2 3 4 5 6 7 
50.95 60.95 70.95 80.95 90.95 100.95 110.95 
50 60 70 80 90 100 110 
28 30 31 34 35 38 40 
28 30 31 34 35 38 40 
28 30 31 34 35 38 40 
1.4 1.5 1.55 1.7 1.75 1.9 2 
1.96 2.25 2.40 2.89 3.06 3.61 4 
25.5 26.7 29.7 27.7 29.4 27.7 27.5 
Mean value of 1/T^{2} = 27.661 cm/s^{2} = 0.276 m/s^{2}
Therefore, Acceleration due to gravity, g = 4π^{2}(1/T^{2}) = 4 x (3.14)^{2} x 0.276 = 10.896 m/s^{2}
l – T^{2} graph
From graph:
AB = 43 cm = 0.43 m
BC = 1.5 s^{2}
G = 4π^{2}(AB/BC) = 4 x (3.14)^{2} x 0.43/1.5 = 11.30 m/s^{2}
Length of the seconds pendulum (OD) = 110 cm = 1.10 m
Period of the pendulum whose length is 105 cm = √OE = 1.92 s
Results
i. l/T^{2} is found to be a constant
ii. Acceleration due to gravity at the place,
(a) by calculation = 10.896 m/s^{2}
(b) from graph = 11.30 m/s^{2}
iii. Length of the seconds pendulum =1.10 m
iv. Period of the pendulum whose length is 105 cm = 1.92 s
Investigatory Project on Air Pollution
Investigatory Project on Study of Pollutants in Air (Class 12)
IntroductionAtmosphere acts as an insulating blanket around the earth. It is the source of essential gases, and it keeps day and night temperatures. It becomes a shield and protects the earth from UV radiations and meteors. Normal composition of clean air in the atmosphere is as follows.