In an experiment it was found that when a sonometer in its fundamental mode of vibration and a tuning fork - Physics - Electromagnetic Waves

Question

In an experiment it was found that when a sonometer in its
fundamental mode of vibration and a tuning fork gave 5 beats when
length of wire is 1 05 mt or 1mt The velocity of transverse waves
in sonometer wire when its length is 1m------------

Somnath physics · Accepted Answer

Let the frequency of the tuning fork be = xFor the fundamental mode of vibration of a string of a sonometer, we have f=12LTm    ---1T=tension, m = mass per unit lengthAgain, velocity of the tranverse waves on the string v=Tm      ---2L1=1 mL2=1
05 mA/qx−v2L2=4  (using eqn
 2) ---3 v2L1−x=4    ---4
Solving eqn  3 and eqn  4
x=v4(1L1+1L2)  ---5 By eqn  4 and eqn
 5v2L1−v4(1L1+1L2)=4=>v2×1−v4(1+11
05)=4=>v=336 ms−1

In an experiment it was found that when a sonometer in its fundamental mode of vibration and a tuning fork gave 5 beats when length of wire is 1.05 mt or 1mt.The velocity of transverse waves in sonometer wire when its length is 1m------------