Two vibrating tuning forks produce progressive waves given Y_1=4 sin 500 π t and Y_2=2 sin 506 π t . Number of beats produced per minute is:

Correct answer: (B) 180. y_1=4 sin 500 π t y_2=2 sin 506 π t ω_1=500 π , ω_2=500 π, ω=2 π v_1=250, v_2=253 ∴ v =v_2-v_1=253-250 =3 beats / s

Q123 / 200 · NEET 2005 · Physics

Two vibrating tuning forks produce progressive waves given $Y_1=4 \sin 500$ $\pi \mathrm{t}$ and $Y_2=2 \sin 506 \pi \mathrm{t}$. Number of beats produced per minute is:

A
360
Correct answer
B
180
C
60
D
3

Solution

$\begin{aligned} & y_1=4 \sin 500 \pi t \\ & y_2=2 \sin 506 \pi t \\ & \omega_1=500 \pi \text {, } \\ & \omega_2=500 \pi, \omega=2 \pi \\ & v_1=250, v_2=253 \\ & \end{aligned}$ $\begin{aligned} \therefore \quad v & =v_2-v_1=253-250 \\ & =3 \mathrm{beats} / \mathrm{s}\end{aligned}$

Hence, the correct answer is option: 'B'.

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