Physics - Sound Wave Question with Solution | TestHub

Let $A_1$ and $A_2$ be the amplitudes of the two waves, and $A_R$ be the resultant amplitude. Given $A_1=A_2=A$ and $A_R=A$.

The formula for resultant amplitude is:

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

Substituting the given values:

$$A=\sqrt{A^2+A^2+2A\cdot A\cos \varphi }$$

$$A^2=2A^2+2A^2\cos \varphi$$

$$A^2=2A^2(1+\cos \varphi )$$

$$1=2(1+\cos \varphi )$$

$$\frac{1}{2}=1+\cos \varphi$$

$$\cos \varphi =\frac{1}{2}-1=-\frac{1}{2}$$

Therefore, $\varphi =\frac{2\pi }{3}$.

The final answer is $\boxed{2\pi /3}$.