Two vibrating tuning forks produce progressive waves given by y_1=4...

To reach the solution the given wave equations must be compared with standard equation of progressive wave. So, $$\begin{aligned} & y_1=4 \sin 500 \pi t...(i) \\ & y_2=2 \sin 506 \pi t...(ii)\end{aligned}$$ 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 $$\begin{aligned} & =f_2-f_1=253-250 \\ & =3\text{ beats } / \mathrm{s} \\ & =3 \times 60 \text{ beats } / \mathrm{min} \\ & =180 \text{ beats } / \mathrm{min}\end{aligned}$$