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 l m Hz = a) For a given m and fixed T. n l µ (or) nl = constant where n → Frequency of the fundamental mode of vibration of the string (Hz) m → Mass per unit length of the string ( kg m – ) 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 Wedge Steel wire Mass hanger Load UNIT- (XI- - ) PRACTICAL FIRST UNIT- (XI- - ) PRACTICAL FIRST - - - - Practical PROCEDURE ¾ Set up the sonometer on the table and clean the groove on the pulley to ensure minimum friction ¾ Stretch the wire by placing suitable mass in the hanger. Keep a small paper rider over the wire, between the two bridges.
¾ Set the tuning fork into vibrations by striking it against the rubber pad and place it over the sonometer,by its stem. ¾ Adjust the vibrating length of the wire by sliding the bridge B till the vibrating sound of the wire is maximum ¾ when the frequency of vibration is in resonance with the frequency of the tuning fork, the paper rider falls down. ¾ The length of the wire between the wedges A and B is measured using meter scale. It is called as resonant length.
¾ Repeat the above procedure for tuning forks of different frequencies by