A uniform wire of length 12 m and mass 6 kg is suspended from a rigid support. A mass of 2 kg is a attached to the lower free end. A transverse wave of length 0 . 0 6 m is generated at the lower end of the wire . What is its wavelength when the wave reaches the upper end ?

A uniform wire of length 12 m and mass 6 kg is suspended from a rigid

1.	A uniform wire of length 12 m and mass 6 kg is suspended from a rigid support. A mass of 2 kg is a attached to the lower free end. A transverse wave of length 0 . 0 6 m is generated at the lower end of the wire . What is its wavelength when the wave reaches the upper end ?
Answer» Solution :Velocity of TRANSVERSE vibration in a stretchedwire, ` V= sqrt((T)/(m))` , where T = tension in the wire and m = mass per unit length = constant, for the uniform wire. If`V_(1) and V_(2)` are the velocities at the lower and upper ends, respectively, `(V_(1))/(V_(2)) = sqrt((T_(1))/(T_(2)))` Here, `T_(1)=`tension at the lower end = weight of the suspended mass ` 2 XX 9. 8 ` N , `T_(2)=`tension at the upper end = weight of the wire and the suspended mass ` = ( 2 + 6) xx 9 . 8 = 8 xx 9 . 8 `N Theentire wire will emit a sound of a FIXED frequency, so the wavelength `lambda` is proportional to the wave velocity V . `:. lambda_(2) = (V_(1))/(V_(2)) = sqrt((T_(1))/(T_(2)))` or,` lambda_(2) = lambda_(1) sqrt((T_(2))/(T_(1))) = 0 . 06 xx sqrt((8 xx 9 . 8)/(2 xx 9 . 8)) = 0 . 12 ` m .