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Q.
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
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 $/ \min$