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
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