Question

Two waves of equal amplitude $A$ and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is

• A. between $0$ and $2A$
  
• B. $A$
• C. $0$
• D. $2A$

Answer 1

The correct option is A between $0$ and $2A$


The resultant amplitude of the two waves is given by
$A_R=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \theta }$,
Here $A_1=A,A_2=A$
$=\sqrt{A^2+A^2+2A^2\cos \theta }$
$=\sqrt{2}A(1+\cos \varphi {)}^{\frac{1}{2}}$
$\varphi =0,A_{max}=2A$
$\varphi =\pi ,A_{min}=0$
$0\le A_R\le 2A$
Final answer: $\left(d\right)$