Answer to Question #164203 in Optics for Ramon

Question

When a tuning fork of frequency 256//z is sounded together with a sonometer wire emitting its

      fundamental frequency, 6 beats are heard every second. When the prongs of the tuning fork are

       highly loaded, 4 beats are heard every second.

      (a.) What is the fundamental frequency of the sonometer wire?

(b.) If the length of the sonometer wire is 25cm, and the mass per unit length of the material of the

wire is 9.0 ×10-3kgm¯¹, calculate the tension in the sonometer wire. 

Answer 1

 frequency of fork $\nu = 256Hz$

$∴ \nu_2 = \nu_1 ± 6 \to 250Hz \space or\space 262HZ$

the fundamental frequency of the sonometer wire is 262HZ

l = 25cm $\rho = 9*10^{-3} kg/m^3$

T = $4ml^2v_1^2 = = 4*9*10^{-3}*625*10^{-4}*262^2 = 155N$