Two waves travel down the same string . These waves have the same velocity , frequency `f` and wavelength but having different phase constants `phi_(1)` and `phi_(2) (lt phi_(1))` and amplitudes `A_(1)` and `A_(2) ( lt A_(1))`. Mark the correct statement(s) for the resultant wave which is produced due to superposition of these two waves.

Options

A. The amplitude of the resultant waves is `A = A_(1) + A_(2)`
B. The amplitude of the resultant waves is `A_(1) - A_(2) to A_(1) + A_(2)`
C. The frequency of the resultant waves is `f`
D. The frequency of the resultant waves is `f//2`

Answer

B, C

Explanation

When two waves having same frequency superimose under given conditions the frequency of the resultant wave is the same as that of component waves . From the theory of interference of waves it can be easily understood . The amplitude of resultant wave for the given situation is given by
`A = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos delta)` where `delta` is the phase difference between the waves , so `A` can be anything between `A_(1) - A_(2) to A_(1) + A_(2)` depending upon the value of `delta`.