The lower end of a homogeneous beam of mass $45\mathrm{.}0$ kg is attached to a wall by means 

of a frictionless hinge. The beam is kept in balance by a horizontal cable 

 is attached to the top end so that the beam forms an angle of $30$ degree with the wall. The cable  

 has a length of $0\mathrm{.}330$ m and a mass of $0\mathrm{.}0920$ kg$.$ The speed of sound is $340$ m$/$s$.$ 

 

 $($a$)$ Determine the cable tension and the reaction force in the hinge. 

 

 $($b$)$ What is the fundamental frequency of transverse standing waves on the cable? 

 

 $($c$)$ What is the frequency and wavelength of the sound produced by the cable vibrating at the fundamental frequency?