Two vibrating tuning forks produce progressive waves given by
$${y_1} = 4\sin 500\,\pi t$$    and $${y_2} = 2\sin 506\,\pi t.$$
Number of beat produced per minute is

Solution :
Given,
$$\eqalign{ & {y_1} = 4\sin 500\,\pi t\,......\left( {\text{i}} \right) \cr & {y_2} = 2\sin 506\,\pi t\,......\left( {{\text{ii}}} \right) \cr} $$
Comparing Eqs. (i) and (ii), we get
$$y = a\sin \omega t\,.......\left( {{\text{iii}}} \right)$$
$$\eqalign{ & {\text{We}}\,{\text{have,}}\,\,{\omega _1} = 500\,\pi \cr & \Rightarrow {n_1} = \frac{{500\,\pi }}{{2\pi }} = 250\,beats/s\,\left[ {\therefore n = \frac{\omega }{{2\pi }}} \right] \cr & {\text{and}}\,\,{\omega _2} = 506\,\pi \cr & \Rightarrow {n_2} = \frac{{506\,\pi }}{{2\,\pi }} = 253\,beats/s \cr} $$
Thus, number of beats produced
$$\eqalign{ & = {n_2} - {n_1} = 253 - 250 = 3\,beats/s \cr & = 3 \times 60\,beats/\min = 180\,beats/\min \cr} $$
NOTE
If equation of wave is given and to find physical quantities like amplitude, wavelength, time period, frequency, just compare the given equation with standard equation of wave.