Physics - Sound Wave Question with Solution | TestHub

To reach the solution the given wave equations must be compared with standard equation of progressive wave. So, $\begin{array}{rl}& y_1=4\sin 500\pi t...(i)\\ & y_2=2\sin 506\pi t...(ii)\end{array}$ Comparing Eqs. (i) and (ii) with $y=a\sin \omega t...(iii)$ We have, ${\omega }_1=500\pi$ $\Rightarrow f_1=\frac{500\pi }{2\pi }=250$ beats $/\mathrm{s}$ and ${\omega }_2=506\pi$ $\Rightarrow f_2=\frac{506\pi }{2\pi }=253$ beats $/\mathrm{s}$ Thus, number of beats produced $\begin{array}{rl}& =f_2-f_1=253-250\\ & =3\text{ beats }/\mathrm{s}\\ & =3\times 60\text{ beats }/\min \\ & =180\text{ beats }/\min \end{array}$