# 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 X-axis and ‘1/l’ along the Y-axis 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.

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 l2 or M/l2 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/l2 = K, a constant i.e., M l2

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 X-axis and l2 along the Y-axis. The graph is found to be a straight line. (M/l2) is calculated.

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 l2 (cm2) M/l2 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/l2 = 0.006

M = l2 x 0.006

= 462.25 x 0.006 = 2.8 kg

Result:

i. l2 — M graph is drawn. The graph is found to be a straight line. Also, (M/l2) is found to be a constant. So, it is concluded that T l2.

ii. Unknown mass = 2.8 kg