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.
Sonometer, six tuning forks of known frequencies, Metre scale, rubber pad, paper rider, hanger with half – kilogram masses, wooden bridges
The frequency n of the fundamental mode of vibration of a string is given by n
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)
SONOMETER - STUDY OF RELATION BETWEEN FREQUENCY AND LENGTH OF A GIVEN WIRE UNDER CONSTANT TENSION USING SONOMETER
· 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.
Tension (constant) on the wire (mass suspended from the hanger including its own mass) T = _______ N
The product nl for all the tuning forks remain constant (last column in the table)
· 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)