Question

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 beats produced per minute is

• A. 360
• B. 180
• C. 3
• D. 60

Answer 1

Answer: (B)

To reach the solution the given wave equations must be compared
with standard equation of progressive wave.
So, $y_1=4\sin 500\pi t$...(i)
$y_2=2\sin 506\pi t$...(ii)
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/s
and ${\omega }_2=506\pi$
$\Rightarrow f_2=\frac{506\pi }{2\pi }=253$ beats/s
Thus, number of beats produced
$=f_2-f_1=253-250$
$=3$ beats / s
$=3\times 60$ beats $/\min$
$=180$ beats $/\min$