Study of Relation Between Frequency and Length of a Given Wire Under Constant Tension Using 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 – kilogram masses, wooden bridges

FORMULA

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

Where

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

m → Mass per unit length of the string ( kg m^–1 )

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

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

M → 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

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

·         Stretch the wire by placing suitable mass in the hanger

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

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

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

·         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.

·         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.

·         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

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

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