Question

Two waves are represented by y₁ = a sin `(omega"t" + pi/6)` and y₂ = a cos `omega"t"`. What will be their resultant amplitude?

Options

• a

• `sqrt(2) "a"`

• `sqrt(3) "a"`

• 2a

Answer 1

`sqrt(3) "a"`

Explanation:

y₁ = a sin  `(omega"t" + pi/6)`  and

y₂ = a cos `omega"t"` = a sin `(omega"t" + pi/2)` 

`therefore "A"_"R" = sqrt("a"^2 + "a"^2 + 2"a"^2 "cos" (pi/2 - pi/6)`

= `sqrt("a"^2 + "a"^2 + 2"a"^2 1/2) = sqrt(3) ` a