Question

Two waves are simultaneously passing through a string and their equations are : $y_1=A_1\sin k(x-vt),y_2=A_2\sin k(x-vt+x_0)$ Given amplitudes $A_1=12\text{mm}$ and $A_2=5\text{mm}$, $x_0=3.5\text{cm}$ and wave number $k=6.28{\text{cm}}^{-1}$. The amplitude of resulting wave will be _____ mm.

• A. 7.00
• B. 7.0
• C. 7

Answer 1

Answer: (A), (B), (C)

$y_1=12\sin 6.28(x-vt)$

$y_2=5\sin 6.28(x-vt+3.5)$

$\Delta \varphi =\frac{2\pi }{\lambda }\left(\Delta x\right)=k\Delta x$

$\Delta \varphi =7\pi$

$A_{net}=\sqrt{{A_1}^2+{A_2}^2+2A_1{A}_2\cos \varphi }$

$A_{net}=\sqrt{{12}^2+5^2+\left(2\right)\left(12\right)\left(5\right)\cos 7\pi }$

$A_{net}=\sqrt{144+25-120}$

$A_{net}=7\text{mm}$