A string of linear mass density is joined at x = L to a string with linear mass density /9 and length 3L to form a composite string of total length 4L. The end of this composite string is fixed at x = 0 and its end at z = 4L is free to oscillate in the ty direction. Show that for the string to be set into vibration with a standing wave pattern, the wavenumber ky in the denser part of the string must obey the following condition √3 sin(k₁ L) = 2 [10]