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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
3
B
360
C
180
D
60
Detailed Solution
Compare each equation with $Y = A\sin 2\pi nt$.
$2\pi n_1 = 500\pi \Rightarrow n_1 = 250$ Hz
$2\pi n_2 = 506\pi \Rightarrow n_2 = 253$ Hz
Number of beats per second $= n_2 - n_1 = 253 - 250 = 3$
Number of beats produced per minute $= 3 \times 60 = 180$
$2\pi n_1 = 500\pi \Rightarrow n_1 = 250$ Hz
$2\pi n_2 = 506\pi \Rightarrow n_2 = 253$ Hz
Number of beats per second $= n_2 - n_1 = 253 - 250 = 3$
Number of beats produced per minute $= 3 \times 60 = 180$