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. On 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 travelling wave having amplitude `a sqrt(2)` will be formed
D. On superposition of (iii) and (iv) , a transverse stationary wave will be formed

Answer

A, D

Explanation

New wave ` = y_(1) hat(j) + z_(1) hat(k)`
` = ( a hat(j) + a hat(k)) sin omega(( t - x)/(v))`
Amplitude ` = | a hat(j) + a hat(k)| = a sqrt(2)`
(i) and (ii) are travelling in opposite directions , so they will form stationary waves.
Similarly (iii) and (iv) will make the stationary wave.