Question

If the two waves represented by $y_1 = 4\, sin\omega t\, m$ and $y_2 = 3sin(\omega t + \pi/3) \,m$ interfere at a point, the amplitude of the resulting wave will be about

• A. $7 \,m$
• B. $5 \,m$
• C. $6 \,m$
• D. $3.5 \,m$

Answer 1

Answer: (C)

$y_{1}=4sin\omega t$
$y_{2}=3sin\left(\omega t+\pi/3\right)$
Here, $a=4\,m$, $b=3\,m$, $\phi=\pi/3$
$R=\sqrt{a^{2}+b^{2}+2ab\,cos\,\phi}$
$=\sqrt{4^{2}+3^{2}+2ab\,cos\,\phi}$
$=\sqrt{4^{2}+3^{2}+2\times4\times3\,cos\,\pi/3}$
$=\sqrt{37}\approx6\,m$