Question

Two progressive waves having equation $x_1=3\sin \omega \tau$ and $x_2=4\sin (\omega \tau ={90}^{\circ })$ are super imposed. The amplitude of the resultant wave is

• A. $5unit$
• B. $1unit$
• C. $3unit$
• D. $4unit$

Answer 1

Answer: (A)

$5unit$

$x_1=2\sin \omega t$
$x_2=4\sin (\omega t+{90}^{\circ })$
The phase difference between the two waves is ${90}^{\circ }$.
So, resultant amplitude
$a=\sqrt{(3{)}^2+(4{)}^2}$
$=\sqrt{9+16}=\sqrt{25}$
$=5unit$