Following are equations of four waves :
(i) `y_(1) = a sin omega ( t - (x)/(v))`
(ii) `y_(2) = a cos omega ( t + (x)/(v))`
(iii) `z_(1) = a sin omega ( t - (x)/(v))`
(iv) `z_(1) = a cos omega ( t + (x)/(v))`
Which of the following statements are correct ?

Options

A. One superposition of waves (i) and (iii), a travelling wave having amplitude `a sqrt(2)` will be formed.
B. Superposition of waves (ii) and (iii) is not possible
C. On superposition of waves (i) and (ii), a transverse stationary wave having maximum amplitude `a sqrt(2)` will be formed.
D. On superposition of waves (iii) and (iv), a transverse stationary wave will be formed.

Answer

A, D

Explanation

Superposition of waves (i) & (iii) will give travelling wave having amplitude of `a sqrt(2)`
[waves are along x-axis but particle displacements are along `y` & z-axis respectively]
`z_(1)+z_(2)=a[sin omega (t-(x)/(v))+sin{omega(t+(x)/(v))+(pi)/(2)}]`.