if the equation  of sound heard by observe is given as $y=8\sin \left(10\pi t\right)\cos \left(2000\pi t\right)atx=0$, then number of beats heard by observe is 2k .Find out the value of  k ?

Given equation is  $y=8\sin \left(10\pi t\right)\cos \left(2000\pi t\right)$
It can be written as  $y=4\sin 2010\pi t-\sin 1990\pi t)$
At x=0.
$f_1=\frac{2010\pi }{2\pi }=1005Hzand{f}_2=\frac{1990\pi }{2\pi }=995Hz.$
Beat frequency  $f=f_1-f_2.$
$\therefore f_{beats}=f_1-f_2=1005-995=10Hz$
Hence k=5