Physics - Sound Wave Question with Solution | TestHub

Given displacements are $x_1=2\sin (1000\pi t)$ and $x_2=3\sin (1006\pi t)$.

The angular frequencies are ${\omega }_1=1000\pi$ and ${\omega }_2=1006\pi$.

The frequencies are $f_1=\frac{{\omega }_1}{2\pi }=500$ Hz and $f_2=\frac{{\omega }_2}{2\pi }=503$ Hz.

The beat frequency is $f_b=|f_1-f_2|=|500-503|=3$ beats/s.

The amplitudes of the waves are $A_1=2$ and $A_2=3$.

The maximum amplitude during interference is $A_{max}=A_1+A_2=2+3=5$.

The maximum intensity is $I_{max}\propto A_{max}^2=5^2=25$ units.

Answer: 3 beats/s with maximum intensity 25 units