Sonometer Experiment with Readings (Class 11)
Sonometer Experiment with Readings (Class 11)
Sonometer Experiment  I
Aim:
i. To show that n x l is a constant
ii. To find the unknown frequency of the given tuning fork.
Apparatus:
Sonometer, Tuning forks. Slotted weights, Rubber hammer etc.
The sonometer consists of a hollow rectangular wooden box with a peg at one end and a smooth vertical pulley at the other end. A wire is attached to the peg and other end carries a weight hanger which passes over the two bridges A and B and the pulley.
Theory:
The frequency (n) of transverse vibration of a string is inversely proportional to the length of the vibrating segment of the wire when tension (T) and linear density (m) are constants.
i.e., n ∝ 1/l
n x l = K, a constant
Unknown frequency n’ = K/l’
Where, l’ = resonating length for the tuning fork whose frequency is to be determined.
Procedure
1. Verification of the law:
The sonometer wire is stretched with a suitable mass M (say 2 kg) by placing on the weight hanger. The bridges A and B are kept close to each other. A thin paper rider is placed on the string between the bridges. The tuning fork of frequency ‘n’ is excited and its stem is pressed on the sonometer box. The bridges are adjusted until the paper rider vibrates with maximum amplitude and is thrown off. The length of the wire between the bridges (l) is measured. The experiment is repeated and the mean length (l) is found out. Then n x l is calculated. The experiment Is repeated with other tuning forks of different frequencies without changing the tension. Each case n x l is found to be a constant (K).
A graph is drawn with frequency ‘n’ along Xaxis and ‘1/l’ along the Yaxis The graph will be a straight line.
(ii) To determine unknown frequency
Using the tuning fork whose frequency is to be determined, resonating length ‘l’ is measured. If n’ is its frequency, then n’ x l’ = K. Thus n’ = K/l’ can be calculated.
Observations and Readings
To study the relation between n and l
Frequency of tuning fork 
Length of wire vibrating in unison 
1/l (cm^{1}) 
nl 

1 
2 
Mean (cm) 

288 
23 
23 
23 
0.0434 
6624 
320 
17.5 
17.7 
17.6 
0.05681 
7497.6 
480 
15.4 
15.6 
15.5 
0.0645 
7440 
Unknown Frequency 
13.1 
13.5 
13.3 
0.0751 

Unknown frequency, x = nl/l’ = 6812.4/13.3 = 512.18 Hz
Results
i. n x l is found to be a constant.
ii. Frequency of the given tuning fork = 512.18 Hz
Sonometer Experiment  II
Aim:
To find the relation between length and tension, for a constant frequency and diameter of a stretched string.
Apparatus:
Sonometer, slotted weights, a tuning fork, paper rider, steel wire, etc.
Theory:
For fixed frequency of a string, the square root of the tension T of the string is directly proportional to the length l of the string. i.e., √T ∝ l. If the tension is in kgwt, M, then, √M ∝ l, i.e., M ∝ l^{2} or M/l^{2} is a constant.
Procedure:
To study the relation between length and tension for a constant frequency.
For a fixed frequency, √T/l is a constant where T is the tension of the string and l is the length of the vibrating segment of the string. If tension is in kg. wt (M),
√M/l = a constant
Therefore, M/l^{2} = K, a constant i.e., M ∝ l^{2}
The sonometer wire is stretched by placing a mass or 1 kg (M) on the weight hanger. The bridges A and B are placed close to each other. A light paper rider is placed on the string between the bridges. The tuning fork is excited and its stem is pressed on the sonometer box between A and B. The length of the vibrating segment is adjusted so that the paper rider vibrates vigorously. This happen when the frequency of the vibrating segment is same as that of the tuning fork. The length of the vibrating segment is measured. The experiment is repeated and the mean l is found out.
The experiment is repeated by keeping weights of 1.5 kg, 2kg … etc., on the weight hanger and the resonating length is found out in each case. A graph is drawn with M along the Xaxis and l^{2} along the Yaxis. The graph is found to be a straight line. (M/l^{2}) is calculated.
Observations and Readings
To study the relation between l and T
Frequency of the tuning fork, n = 288 Hz
Tension (M kgwt) 
Length of wire vibrating in unison 
l^{2} (cm^{2}) 
M/l^{2} 

1 
2 
Mean l (cm) 

1 
14.54 
14.56 
14.55 
211.7 
0.0047 
1.5 
15.5 
15.7 
15.6 
243.66 
0.0616 
2 
17.5 
17.8 
17.65 
311.52 
0.0064 
Unknown Mass 
21.4 
21.6 
21.5 
462.25 

Unknown mass, M/l^{2} = 0.006
M = l^{2} x 0.006
= 462.25 x 0.006 = 2.8 kg
Result:
i. l^{2} — M graph is drawn. The graph is found to be a straight line. Also, (M/l^{2}) is found to be a constant. So, it is concluded that T ∝ l^{2}.
ii. Unknown mass = 2.8 kg
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