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# Study of Relation Between Frequency and Length of a Given Wire Under Constant Tension Using Sonometer

To study the relation between frequency and length of a given wire under constant tension using a sonometer.

STUDY OF RELATION BETWEEN FREQUENCY AND LENGTH OF A GIVEN WIRE UNDER CONSTANT TENSION USING SONOMETER

## AIM

To study the relation between frequency and length of a given wire under constant tension using a sonometer.

## APPARATUS REQUIRED

Sonometer, six tuning forks of known frequencies, Metre scale, rubber pad, paper rider, hanger with half ŌĆō kilogram masses, wooden bridges

## FORMULA

The frequency n of the fundamental mode of vibration of a string is given by n Where

n ŌåÆ Frequency of the fundamental mode of vibration of the string (Hz)

m ŌåÆ Mass per unit length of the string ( kg mŌĆō1 )

l ŌåÆ Length of the string between the wedges (m)

T ŌåÆ Tension in the string (including the mass of the hanger) = Mg ( N )

M ŌåÆ Mass suspended, including the mass of the hanger (Kg)

## DIAGRAM SONOMETER - STUDY OF RELATION BETWEEN FREQUENCY AND LENGTH OF A GIVEN WIRE UNDER CONSTANT TENSION USING SONOMETER

## PROCEDURE

┬Ę         Set up the sonometer on the table and clean the groove on the pulley to ensure minimum friction

┬Ę         Stretch the wire by placing suitable mass in the hanger

┬Ę         Set the tuning fork into vibrations by striking it against the rubber pad. Plug the sonometer wire and compare the two sounds.

┬Ę         Adjust the vibrating length of the wire by sliding the bridge B till the sounds appear alike.

┬Ę         For the final adjustment, place a small paper rider R in the middle of the wire AB.

┬Ę         Sound the tuning fork and place its shank stem on the bridge A or on the sonometer box and slowly adjust the position of bridge B until the paper rider is agitated violently indicating resonance.

┬Ę         The length of the wire between the wedges A and B is measured using meter scale. It is the resonant length. Now the frequency of vibration of the fundamental mode equals the fre-quency of the tuning fork.

┬Ę         Repeat the above procedure for other tuning forks by keeping the same load in the hanger.

## OBSERVATIONS

Tension (constant) on the wire (mass suspended from the hanger including its own mass) T = _______ N ## GRAPH: ## CALCULATION

The product nl for all the tuning forks remain constant (last column in the table)

## RESULT

┬Ę           For a given tension, the resonant length of a given stretched string varies as reciprocal of the frequency (i.e., n ŌłØ 1/l)

┬Ę           The product nl is a constant and found to be ______ (Hz m)

Tags : Physics Laboratory Practical Experiment , 11th Physics : Practical Experiment
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11th Physics : Practical Experiment : Study of Relation Between Frequency and Length of a Given Wire Under Constant Tension Using Sonometer | Physics Laboratory Practical Experiment