Question

A wave has shm whose period is 4s while another wave which also possess shm has its period 3s.if both are combined will be the resultant wave will have time period equal to

Answer 1

Just multiply them.....

T= t1 × t2

= 4×3

= 12 s

Answer 2

concept :- when two periodic functions f(x), and g(x) are given in such a way that t and T are period of these functions respectively.
then, period of h(x) = g(x) ± f(x) is LCM of t and T.


now come to the question,
period of 1st SHM, $T_1$ = 4s
period of 2nd SHM, $T_2$ = 3s

from above explanation,
period of combination of given SHM's = LCM of $T_1$ and $T_2$
= LCM of 4s and 3s
= 12s

hence, period of resultant SHM is 12s.