Two waves represented by y = a sin (ωt −&#

Question

Two waves represented by

y = a s i n (ω t - k x)

and

y = a c o s (ω t - k x)

are superimposed. The resultant wave will have an amplitude

Options:

A . a

B . √2a

C . 2a

D . 0

Answer: Option B
:
B
The two waves are obviously at a phase difference of

\frac{π}{2}

so the resultant amplitude

A = \sqrt{a^{2} + a^{2} + 2. a . a c o s \frac{π}{2}} = \sqrt{2} a

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