Two vibrating tuning forks produce progressive waves given by ${Y}_{1}=4\mathrm{sin}500\pi t$ and ${Y}_{2}=2\mathrm{sin}506\pi t.$ Number of beats produced per minute is

(1) 360

(2) 180

(3) 3

(4) 60

(2) From the given equations of progressive waves ${\omega }_{1}=500\pi$ and ${\omega }_{2}=506\pi$

${n}_{1}=250$ and ${n}_{2}=253$

So beat frequency $={n}_{2}-{n}_{1}=253-250=3$ beats per sec

∴ Number of beats per min = 180.

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