Question

Beats are produced because of the superposition of two progressive notes> Maximum loudness at the waxing is $n$ times the loudness of either notes. What is the values of $n$?

• A. $4$
• B. $2$
• C. $\sqrt{2}$
• D. $1$

Answer 1

The correct option is A $4$

Resultant amplitude is $A=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \left(\varphi \right)}$, where

$\varphi$ is the angle between the superposing waves.

$A=A_{max}=A_1+A_2$, when $\cos \left(\varphi \right)=1$.

So, maximum loudness $I_{max}=A_{max}^2=(A_1+A_2{)}^2=4A_0^2=4I_0$,

assuming that the waves have same amplitude $A_0$.