Question

Determine the magnitude of the resultant amplitude for the interference of two similar waves when the phase difference between them is ${45}^{\circ }$. Given that, amplitudes of both sources are $A_1=3\text{cm},A_2=4\text{cm}$.

• A. $3.5\text{cm}$
• B. $4.5\text{cm}$
• C. $6.5\text{cm}$
• D. $7.5\text{cm}$

Answer 1

The correct option is C $6.5\text{cm}$

The resultant amplitude for a wave is given by,

$A=\sqrt{{A_1}^2+{A_2}^2+2A_1{A}_2\cos \alpha }$

$\Rightarrow A=\sqrt{3^2+4^2+2\times 3\times 4\cos {45}^{\circ }}$

$\Rightarrow A=6.5\text{cm}$

Hence, option $\left(C\right)$ is the correct answer.